/usr/include/deal.II/dofs/dof_tools.h is in libdeal.ii-dev 6.3.1-1.1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 | //---------------------------------------------------------------------------
// $Id: dof_tools.h 21358 2010-06-24 23:38:14Z bangerth $
// Version: $Name$
//
// Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 by the deal.II authors
//
// This file is subject to QPL and may not be distributed
// without copyright and license information. Please refer
// to the file deal.II/doc/license.html for the text and
// further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__dof_tools_h
#define __deal2__dof_tools_h
#include <base/config.h>
#include <base/exceptions.h>
#include <base/table.h>
#include <base/index_set.h>
#include <lac/constraint_matrix.h>
#include <dofs/function_map.h>
#include <vector>
#include <set>
#include <map>
DEAL_II_NAMESPACE_OPEN
template<int dim, class T> class Table;
class SparsityPattern;
template <typename number> class Vector;
template <int dim> class Function;
template <int dim> class Point;
template <int dim, int spacedim> class FiniteElement;
template <int dim, int spacedim> class DoFHandler;
namespace hp
{
template <int dim, int spacedim> class DoFHandler;
}
template <int dim, int spacedim> class MGDoFHandler;
class ConstraintMatrix;
template <class GridClass> class InterGridMap;
template <int dim, int spacedim> class Mapping;
//TODO: map_support_points_to_dofs should generate a multimap, rather than just a map, since several dofs may be located at the same support point
/**
* This is a collection of functions operating on, and manipulating
* the numbers of degrees of freedom. The documentation of the member
* functions will provide more information, but for functions that
* exist in multiple versions, there are sections in this global
* documentation stating some commonalities.
*
* All member functions are static, so there is no need to create an
* object of class DoFTools.
*
*
* <h3>Setting up sparsity patterns</h3>
*
* When assembling system matrices, the entries are usually of the form
* $a_{ij} = a(\phi_i, \phi_j)$, where $a$ is a bilinear functional, often an
* integral. When using sparse matrices, we therefore only need to reserve space
* for those $a_{ij}$ only, which are nonzero, which is the same as to say that
* the basis functions $\phi_i$ and $\phi_j$ have a nonempty intersection of
* their support. Since the support of basis functions is bound only on cells
* on which they are located or to which they are adjacent, to
* determine the sparsity pattern it is sufficient to loop over all
* cells and connect all basis functions on each cell with all other
* basis functions on that cell. There may be finite elements for
* which not all basis functions on a cell connect with each other,
* but no use of this case is made since no examples where this occurs
* are known to the author.
*
*
* <h3>DoF numberings on boundaries</h3>
*
* When projecting the traces of functions to the boundary or parts thereof,
* one needs to build matrices and vectors that act only on those degrees of
* freedom that are located on the boundary, rather than on all degrees of
* freedom. One could do that by simply building matrices in which the entries
* for all interior DoFs are zero, but such matrices are always very rank
* deficient and not very practical to work with.
*
* What is needed instead in this case is a numbering of the boundary degrees
* of freedom, i.e. we should enumerate all the degrees of freedom that are
* sitting on the boundary, and exclude all other (interior) degrees of
* freedom. The map_dof_to_boundary_indices() function does exactly this: it
* provides a vector with as many entries as there are degrees of freedom on
* the whole domain, with each entry being the number in the numbering of the
* boundary or DoFHandler::invalid_dof_index if the dof is not on the
* boundary.
*
* With this vector, one can get, for any given degree of freedom, a unique
* number among those DoFs that sit on the boundary; or, if your DoF was
* interior to the domain, the result would be DoFHandler::invalid_dof_index.
* We need this mapping, for example, to build the mass matrix on the boundary
* (for this, see make_boundary_sparsity_pattern() function, the corresponding
* section below, as well as the MatrixCreator class documentation).
*
* Actually, there are two map_dof_to_boundary_indices() functions, one
* producing a numbering for all boundary degrees of freedom and one producing
* a numbering for only parts of the boundary, namely those parts for which
* the boundary indicator is listed in a set of indicators given to the
* function. The latter case is needed if, for example, we would only want to
* project the boundary values for the Dirichlet part of the boundary. You
* then give the function a list of boundary indicators referring to Dirichlet
* parts on which the projection is to be performed. The parts of the boundary
* on which you want to project need not be contiguous; however, it is not
* guaranteed that the indices of each of the boundary parts are continuous,
* i.e. the indices of degrees of freedom on different parts may be
* intermixed.
*
* Degrees of freedom on the boundary but not on one of the specified
* boundary parts are given the index DoFHandler::invalid_dof_index, as if
* they were in the interior. If no boundary indicator was given or if
* no face of a cell has a boundary indicator contained in the given
* list, the vector of new indices consists solely of
* DoFHandler::invalid_dof_index.
*
* (As a side note, for corner cases: The question what a degree of freedom on
* the boundary is, is not so easy. It should really be a degree of freedom
* of which the respective basis function has nonzero values on the
* boundary. At least for Lagrange elements this definition is equal to the
* statement that the off-point, or what deal.II calls support_point, of the
* shape function, i.e. the point where the function assumes its nominal value
* (for Lagrange elements this is the point where it has the function value
* 1), is located on the boundary. We do not check this directly, the
* criterion is rather defined through the information the finite element
* class gives: the FiniteElement class defines the numbers of basis functions
* per vertex, per line, and so on and the basis functions are numbered after
* this information; a basis function is to be considered to be on the face of
* a cell (and thus on the boundary if the cell is at the boundary) according
* to it belonging to a vertex, line, etc but not to the interior of the
* cell. The finite element uses the same cell-wise numbering so that we can
* say that if a degree of freedom was numbered as one of the dofs on lines,
* we assume that it is located on the line. Where the off-point actually is,
* is a secret of the finite element (well, you can ask it, but we don't do it
* here) and not relevant in this context.)
*
*
* <h3>Setting up sparsity patterns for boundary matrices</h3>
*
* In some cases, one wants to only work with DoFs that sit on the
* boundary. One application is, for example, if rather than interpolating
* non-homogenous boundary values, one would like to project them. For this,
* we need two things: a way to identify nodes that are located on (parts of)
* the boundary, and a way to build matrices out of only degrees of freedom
* that are on the boundary (i.e. much smaller matrices, in which we do not
* even build the large zero block that stems from the fact that most degrees
* of freedom have no support on the boundary of the domain). The first of
* these tasks is done by the map_dof_to_boundary_indices() function of this
* class (described above).
*
* The second part requires us first to build a sparsity pattern for the
* couplings between boundary nodes, and then to actually build the components
* of this matrix. While actually computing the entries of these small
* boundary matrices is discussed in the MatrixCreator class, the creation of
* the sparsity pattern is done by the create_boundary_sparsity_pattern()
* function. For its work, it needs to have a numbering of all those degrees
* of freedom that are on those parts of the boundary that we are interested
* in. You can get this from the map_dof_to_boundary_indices() function. It
* then builds the sparsity pattern corresponding to integrals like
* $\int_\Gamma \varphi_{b2d(i)} \varphi_{b2d(j)} dx$, where $i$ and $j$ are
* indices into the matrix, and $b2d(i)$ is the global DoF number of a degree
* of freedom sitting on a boundary (i.e., $b2d$ is the inverse of the mapping
* returned by map_dof_to_boundary_indices() function).
*
*
* @ingroup dofs
* @author Wolfgang Bangerth, Guido Kanschat and others, 1998 - 2008
*/
class DoFTools
{
public:
/**
* The flags used in tables by certain
* <tt>make_*_pattern</tt>
* functions to determine whether
* two components of the solution
* couple in the interior of mesh
* cells or at the boundary.
*/
enum Coupling
{
/**
* The two components do not
* couple.
*/
none,
/**
* The two components do couple.
*/
always,
/**
* The two components couple only
* if their shape functions can be
* nonzero on this face.
*/
nonzero
};
/**
* @name Auxiliary functions
* @{
*/
/**
* Maximal number of degrees of
* freedom on a cell.
*/
template <int dim, int spacedim>
static unsigned int
max_dofs_per_cell (const DoFHandler<dim,spacedim> &dh);
template <int dim, int spacedim>
static unsigned int
max_dofs_per_cell (const hp::DoFHandler<dim,spacedim> &dh);
/**
* Maximal number of degrees of
* freedom on a face.
*
* This function exists for both non-hp
* and hp DoFHandlers, to allow for a
* uniform interface to query this
* property.
*/
template <int dim, int spacedim>
static unsigned int
max_dofs_per_face (const DoFHandler<dim,spacedim> &dh);
/**
* Maximal number of degrees of
* freedom on a face.
*
* This function exists for both non-hp
* and hp DoFHandlers, to allow for a
* uniform interface to query this
* property.
*/
template <int dim, int spacedim>
static unsigned int
max_dofs_per_face (const hp::DoFHandler<dim,spacedim> &dh);
/**
* Maximal number of degrees of
* freedom on a vertex.
*
* This function exists for both non-hp
* and hp DoFHandlers, to allow for a
* uniform interface to query this
* property.
*/
template <int dim, int spacedim>
static unsigned int
max_dofs_per_vertex (const DoFHandler<dim,spacedim> &dh);
/**
* Maximal number of degrees of
* freedom on a vertex.
*
* This function exists for both non-hp
* and hp DoFHandlers, to allow for a
* uniform interface to query this
* property.
*/
template <int dim, int spacedim>
static unsigned int
max_dofs_per_vertex (const hp::DoFHandler<dim,spacedim> &dh);
/**
* Number of vector components in the
* finite element object used by this
* DoFHandler.
*
* This function exists for both non-hp
* and hp DoFHandlers, to allow for a
* uniform interface to query this
* property.
*/
template <int dim, int spacedim>
static unsigned int
n_components (const DoFHandler<dim,spacedim> &dh);
/**
* Number of vector components in the
* finite element object used by this
* DoFHandler.
*
* This function exists for both non-hp
* and hp DoFHandlers, to allow for a
* uniform interface to query this
* property.
*/
template <int dim, int spacedim>
static unsigned int
n_components (const hp::DoFHandler<dim,spacedim> &dh);
/**
* Find out whether the FiniteElement
* used by this DoFHandler is primitive
* or not.
*
* This function exists for both non-hp
* and hp DoFHandlers, to allow for a
* uniform interface to query this
* property.
*/
template <int dim, int spacedim>
static unsigned int
fe_is_primitive (const DoFHandler<dim,spacedim> &dh);
/**
* Find out whether the FiniteElement
* used by this DoFHandler is primitive
* or not.
*
* This function exists for both non-hp
* and hp DoFHandlers, to allow for a
* uniform interface to query this
* property.
*/
template <int dim, int spacedim>
static unsigned int
fe_is_primitive (const hp::DoFHandler<dim,spacedim> &dh);
/**
* @}
*/
/**
* @name Sparsity Pattern Generation
* @{
*/
/**
* Locate non-zero entries of the
* system matrix.
*
* This function computes the
* possible positions of non-zero
* entries in the global system
* matrix. We assume that a
* certain finite element basis
* function is non-zero on a cell
* only if its degree of freedom
* is associated with the
* interior, a face, an edge or a
* vertex of this cell. As a
* result, the matrix entry
* between two basis functions
* can be non-zero only if they
* correspond to degrees of
* freedom of at least one common
* cell. Therefore,
* @p make_sparsity_pattern just
* loops over all cells and
* enters all couplings local to
* that cell. As the generation
* of the sparsity pattern is
* irrespective of the equation
* which is solved later on, the
* resulting sparsity pattern is
* symmetric.
*
* Remember using
* SparsityPattern::compress()
* after generating the pattern.
*
* The actual type of the
* sparsity pattern may be
* SparsityPattern,
* CompressedSparsityPattern,
* BlockSparsityPattern,
* BlockCompressedSparsityPattern,
* BlockCompressedSetSparsityPattern,
* BlockCompressedSimpleSparsityPattern,
* or any other class that
* satisfies similar
* requirements. It is assumed
* that the size of the sparsity
* pattern matches the number of
* degrees of freedom and that
* enough unused nonzero entries
* are left to fill the sparsity
* pattern. The nonzero entries
* generated by this function are
* overlaid to possible previous
* content of the object, that is
* previously added entries are
* not deleted.
*
* Since this process is purely local,
* the sparsity pattern does not provide
* for entries introduced by the
* elimination of hanging nodes. They
* have to be taken care of by a call to
* ConstraintMatrix::condense()
* afterwards.
*
* Alternatively, the constraints on
* degrees of freedom can already be
* taken into account at the time of
* creating the sparsity pattern. For
* this, pass the ConstraintMatrix object
* as the third argument to the current
* function. No call to
* ConstraintMatrix::condense() is then
* necessary. This process is explained
* in step-27.
*
* In case the constraints are
* already taken care of in this
* function, it is possible to
* neglect off-diagonal entries
* in the sparsity pattern. When
* using
* ConstraintMatrix::distribute_local_to_global
* during assembling, no entries
* will ever be written into
* these matrix position, so that
* one can save some computing
* time in matrix-vector products
* by not even creating these
* elements. In that case, the
* variable
* <tt>keep_constrained_dofs</tt>
* needs to be set to
* <tt>false</tt>.
*
* If the @p subdomain_id parameter is
* given, the sparsity pattern is built
* only on cells that have a subdomain_id
* equal to the given argument. This is
* useful in parallel contexts where the
* matrix and sparsity pattern (for
* example a
* TrilinosWrappers::SparsityPattern) may
* be distributed and not every MPI
* process needs to build the entire
* sparsity pattern; in that case, it is
* sufficient if every process only
* builds that part of the sparsity
* pattern that corresponds to the
* subdomain_id for which it is
* responsible.
*/
template <class DH, class SparsityPattern>
static
void
make_sparsity_pattern (const DH &dof,
SparsityPattern &sparsity_pattern,
const ConstraintMatrix &constraints = ConstraintMatrix(),
const bool keep_constrained_dofs = true,
const unsigned int subdomain_id = numbers::invalid_unsigned_int);
/**
* Locate non-zero entries for
* vector valued finite elements.
* This function does mostly the
* same as the previous
* @p make_sparsity_pattern, but
* it is specialized for vector
* finite elements and allows to
* specify which variables couple
* in which equation. For
* example, if wanted to solve
* the Stokes equations,
* @verbatim
* -\Delta \vec u + \nabla p = 0,
* \div u = 0
* @endverbatim
* in two space dimensions,
* using stable Q2/Q1 mixed
* elements (using the FESystem
* class), then you don't want
* all degrees of freedom to
* couple in each equation. You
* rather may want to give the
* following pattern of
* couplings:
* @verbatim
* 1 0 1
* 0 1 1
* 1 1 0
* @endverbatim
* where "1" indicates that two
* variables (i.e. components of
* the FESystem) couple in the
* respective equation, and a "0"
* means no coupling, in which
* case it is not necessary to
* allocate space in the matrix
* structure. Obviously, the mask
* refers to components of the
* composed FESystem, rather
* than to the degrees of freedom
* contained in there.
*
* This function is designed to
* accept a coupling pattern, like the one
* shown above, through the
* @p couplings parameter, which
* contains values of type #Coupling. It
* builds the matrix structure
* just like the previous
* function, but does not create
* matrix elements if not
* specified by the coupling pattern. If the
* couplings are symmetric, then so
* will be the resulting sparsity
* pattern.
*
* The actual type of the
* sparsity pattern may be
* SparsityPattern,
* CompressedSparsityPattern,
* BlockSparsityPattern,
* BlockCompressedSparsityPattern,
* BlockCompressedSetSparsityPattern,
* or any other class that
* satisfies similar
* requirements.
*
* There is a complication if
* some or all of the shape
* functions of the finite
* element in use are non-zero in
* more than one component (in
* deal.II speak: they are
* non-primitive). In this case,
* the coupling element
* correspoding to the first
* non-zero component is taken
* and additional ones for this
* component are ignored.
*
* Not implemented for
* hp::DoFHandler.
*
* As mentioned before, the
* creation of the sparsity
* pattern is a purely local
* process and the sparsity
* pattern does not provide for
* entries introduced by the
* elimination of hanging
* nodes. They have to be taken
* care of by a call to
* ConstraintMatrix::condense()
* afterwards.
*
* Alternatively, the constraints
* on degrees of freedom can
* already be taken into account
* at the time of creating the
* sparsity pattern. For this,
* pass the ConstraintMatrix
* object as the third argument
* to the current function. No
* call to
* ConstraintMatrix::condense()
* is then necessary. This
* process is explained in @ref
* step_27 "step-27".
*
* In case the constraints are
* already taken care of in this
* function, it is possible to
* neglect off-diagonal entries
* in the sparsity pattern. When
* using
* ConstraintMatrix::distribute_local_to_global
* during assembling, no entries
* will ever be written into
* these matrix position, so that
* one can save some computing
* time in matrix-vector products
* by not even creating these
* elements. In that case, the
* variable
* <tt>keep_constrained_dofs</tt>
* needs to be set to
* <tt>false</tt>.
*
* If the @p subdomain_id parameter is
* given, the sparsity pattern is built
* only on cells that have a subdomain_id
* equal to the given argument. This is
* useful in parallel contexts where the
* matrix and sparsity pattern (for
* example a
* TrilinosWrappers::SparsityPattern) may
* be distributed and not every MPI
* process needs to build the entire
* sparsity pattern; in that case, it is
* sufficient if every process only
* builds that part of the sparsity
* pattern that corresponds to the
* subdomain_id for which it is
* responsible.
*/
template <class DH, class SparsityPattern>
static
void
make_sparsity_pattern (const DH &dof,
const Table<2, Coupling> &coupling,
SparsityPattern &sparsity_pattern,
const ConstraintMatrix &constraints = ConstraintMatrix(),
const bool keep_constrained_dofs = true,
const unsigned int subdomain_id = numbers::invalid_unsigned_int);
/**
* @deprecated This is the old
* form of the previous
* function. It generates a table
* of DoFTools::Coupling values
* (where a <code>true</code>
* value in the mask is
* translated into a
* Coupling::always value in the
* table) and calls the function
* above.
*/
template <class DH, class SparsityPattern>
static
void
make_sparsity_pattern (const DH &dof,
const std::vector<std::vector<bool> > &mask,
SparsityPattern &sparsity_pattern);
/**
* Construct a sparsity pattern that
* allows coupling degrees of freedom on
* two different but related meshes.
*
* The idea is that if the two given
* DoFHandler objects correspond to two
* different meshes (and potentially to
* different finite elements used on
* these cells), but that if the two
* triangulations they are based on are
* derived from the same coarse mesh
* through hierarchical refinement, then
* one may set up a problem where one
* would like to test shape functions
* from one mesh against the shape
* functions from another mesh. In
* particular, this means that shape
* functions from a cell on the first
* mesh are tested against those on the
* second cell that are located on the
* corresponding cell; this
* correspondence is something that the
* IntergridMap class can determine.
*
* This function then constructs a
* sparsity pattern for which the degrees
* of freedom that represent the rows
* come from the first given DoFHandler,
* whereas the ones that correspond to
* columns come from the second
* DoFHandler.
*/
template <class DH, class SparsityPattern>
static
void
make_sparsity_pattern (const DH &dof_row,
const DH &dof_col,
SparsityPattern &sparsity);
/**
* Create the sparsity pattern for
* boundary matrices. See the general
* documentation of this class for more
* information.
*
* The actual type of the sparsity
* pattern may be SparsityPattern,
* CompressedSparsityPattern,
* BlockSparsityPattern,
* BlockCompressedSparsityPattern,
* BlockCompressedSetSparsityPattern, or
* any other class that satisfies similar
* requirements. It is assumed that the
* size of the sparsity pattern is
* already correct.
*/
template <class DH, class SparsityPattern>
static void
make_boundary_sparsity_pattern (const DH &dof,
const std::vector<unsigned int> &dof_to_boundary_mapping,
SparsityPattern &sparsity_pattern);
/**
* Write the sparsity structure of the
* matrix composed of the basis functions
* on the boundary into the
* matrix structure. In contrast to the
* previous function, only those parts
* of the boundary are considered of which
* the boundary indicator is listed in the
* set of numbers passed to this function.
*
* In fact, rather than a @p set
* of boundary indicators, a
* @p map needs to be passed,
* since most of the functions
* handling with boundary
* indicators take a mapping of
* boundary indicators and the
* respective boundary
* functions. The boundary
* function, however, is ignored
* in this function. If you have
* no functions at hand, but only
* the boundary indicators, set
* the function pointers to null
* pointers.
*
* For the type of the sparsity
* pattern, the same holds as
* said above.
*/
template <class DH, class SparsityPattern>
static void
make_boundary_sparsity_pattern (const DH &dof,
const typename FunctionMap<DH::space_dimension>::type &boundary_indicators,
const std::vector<unsigned int> &dof_to_boundary_mapping,
SparsityPattern &sparsity);
/**
* Generate sparsity pattern for
* fluxes, i.e. formulations of
* the discrete problem with
* discontinuous elements which
* couple across faces of cells.
* This is a replacement of the
* function
* @p make_sparsity_pattern for
* discontinuous methods. Since
* the fluxes include couplings
* between neighboring elements,
* the normal couplings and these
* extra matrix entries are
* considered.
*/
template<class DH, class SparsityPattern>
static void
make_flux_sparsity_pattern (const DH &dof_handler,
SparsityPattern &sparsity_pattern);
/**
* This function does the same as
* the other with the same name,
* but it gets two additional
* coefficient matrices. A matrix
* entry will only be generated
* for two basis functions, if
* there is a non-zero entry
* linking their associated
* components in the coefficient
* matrix.
*
* There is one matrix for
* couplings in a cell and one
* for the couplings occuring in
* fluxes.
*
* Not implemented for
* hp::DoFHandler.
*/
template <class DH, class SparsityPattern>
static void
make_flux_sparsity_pattern (const DH &dof,
SparsityPattern &sparsity,
const Table<2,Coupling> &int_mask,
const Table<2,Coupling> &flux_mask);
//@}
/**
* @name Hanging Nodes
* @{
*/
/**
* Compute the constraints resulting from
* the presence of hanging nodes. Hanging
* nodes are best explained using a small
* picture:
*
* @image html hanging_nodes.png
*
* In order to make a finite element
* function globally continuous, we have
* to make sure that the dark red nodes
* have values that are compatible with
* the adjacent yellow nodes, so that the
* function has no jump when coming from
* the small cells to the large one at
* the top right. We therefore have to
* add conditions that constrain those
* "hanging nodes".
*
* The object into
* which these are inserted is
* later used to condense the
* global system matrix and right
* hand side, and to extend the
* solution vectors from the true
* degrees of freedom also to the
* constraint nodes. This
* function is explained in
* detail in the @ref step_6
* "step-6" tutorial program and
* is used in almost all
* following programs as well.
*
* This function does not clear
* the constraint matrix object
* before use, in order to allow
* adding constraints from
* different sources to the same
* object. You therefore need to
* make sure it contains only
* constraints you still want;
* otherwise call the
* ConstraintMatrix::clear()
* function. Likewise, this
* function does not close the
* object since you may want to
* enter other constraints later
* on yourself.
*
* In the hp-case, i.e. when the
* argument is of type
* hp::DoFHandler, we consider
* constraints due to different
* finite elements used on two
* sides of a face between cells
* as hanging nodes as well. In
* other words, for hp finite
* elements, this function
* computes all constraints due
* to differing mesh sizes (h) or
* polynomial degrees (p) between
* adjacent cells.
*
* The template argument (and by
* consequence the type of the
* first argument to this
* function) can be either a
* ::DoFHandler, hp::DoFHandler,
* or MGDoFHandler.
*/
template <class DH>
static void
make_hanging_node_constraints (const DH &dof_handler,
ConstraintMatrix &constraints);
//@}
/**
* Take a vector of values which live on
* cells (e.g. an error per cell) and
* distribute it to the dofs in such a
* way that a finite element field
* results, which can then be further
* processed, e.g. for output. You should
* note that the resulting field will not
* be continuous at hanging nodes. This
* can, however, easily be arranged by
* calling the appropriate @p distribute
* function of a ConstraintMatrix
* object created for this
* DoFHandler object, after the
* vector has been fully assembled.
*
* It is assumed that the number
* of elements in @p cell_data
* equals the number of active
* cells and that the number of
* elements in @p dof_data equals
* <tt>dof_handler.n_dofs()</tt>.
*
* Note that the input vector may
* be a vector of any data type
* as long as it is convertible
* to @p double. The output
* vector, being a data vector on
* a DoF handler, always consists of
* elements of type @p double.
*
* In case the finite element
* used by this DoFHandler
* consists of more than one
* component, you need to specify
* which component in the output
* vector should be used to store
* the finite element field in;
* the default is zero (no other
* value is allowed if the finite
* element consists only of one
* component). All other
* components of the vector
* remain untouched, i.e. their
* contents are not changed.
*
* This function cannot be used
* if the finite element in use
* has shape functions that are
* non-zero in more than one
* vector component (in deal.II
* speak: they are
* non-primitive).
*/
template <class DH, typename Number>
static void
distribute_cell_to_dof_vector (const DH &dof_handler,
const Vector<Number> &cell_data,
Vector<double> &dof_data,
const unsigned int component = 0);
/**
* Extract the indices of the
* degrees of freedom belonging
* to certain vector components
* or blocks (if the last
* argument is <tt>true</tt>) of
* a vector-valued finite
* element. The bit vector @p
* select defines, which
* components or blocks of an
* FESystem are to be extracted
* from the DoFHandler @p
* dof. The entries in @p
* selected_dofs corresponding to
* degrees of freedom belonging
* to these components are then
* flagged @p true, while all
* others are set to @p false.
*
* The size of @p select must
* equal the number of components
* or blocks in the FiniteElement
* used by @p dof, depending on
* the argument
* <tt>blocks</tt>. The size of
* @p selected_dofs must equal
* DoFHandler::n_dofs(). Previous
* contents of this array are
* overwritten.
*
* If the finite element under
* consideration is not
* primitive, that is some or all
* of its shape functions are
* non-zero in more than one
* vector component (which holds,
* for example, for FE_Nedelec or
* FE_RaviartThomas elements), then
* shape functions cannot be
* associated with a single
* vector component. In this
* case, if <em>one</em> shape
* vector component of this
* element is flagged in
* @p component_select, then
* this is equivalent to
* selecting <em>all</em> vector
* components corresponding to
* this non-primitive base
* element.
*/
template <int dim, int spacedim>
static void
extract_dofs (const DoFHandler<dim,spacedim> &dof_handler,
const std::vector<bool> &select,
std::vector<bool> &selected_dofs,
const bool blocks = false);
/**
* The same function as above,
* but for a hp::DoFHandler.
*/
template <int dim, int spacedim>
static void
extract_dofs (const hp::DoFHandler<dim,spacedim> &dof_handler,
const std::vector<bool> &select,
std::vector<bool> &selected_dofs,
const bool blocks = false);
/**
* Do the same thing as
* extract_dofs() for one level
* of a multi-grid DoF numbering.
*/
template <int dim, int spacedim>
static void
extract_level_dofs (const unsigned int level,
const MGDoFHandler<dim,spacedim> &dof,
const std::vector<bool> &select,
std::vector<bool> &selected_dofs,
const bool blocks = false);
/**
* Extract all degrees of freedom
* which are at the boundary and
* belong to specified components
* of the solution. The function
* returns its results in the
* last non-default-valued
* parameter which contains
* @p true if a degree of
* freedom is at the boundary and
* belongs to one of the selected
* components, and @p false
* otherwise.
*
* By specifying the
* @p boundary_indicator
* variable, you can select which
* boundary indicators the faces
* have to have on which the
* degrees of freedom are located
* that shall be extracted. If it
* is an empty list, then all
* boundary indicators are
* accepted.
*
* The size of @p component_select
* shall equal the number of
* components in the finite
* element used by @p dof. The
* size of @p selected_dofs shall
* equal
* <tt>dof_handler.n_dofs()</tt>. Previous
* contents of this array or
* overwritten.
*
* Using the usual convention, if
* a shape function is non-zero
* in more than one component
* (i.e. it is non-primitive),
* then the element in the
* component mask is used that
* corresponds to the first
* non-zero components. Elements
* in the mask corresponding to
* later components are ignored.
*/
template <class DH>
static void
extract_boundary_dofs (const DH &dof_handler,
const std::vector<bool> &component_select,
std::vector<bool> &selected_dofs,
const std::set<unsigned char> &boundary_indicators = std::set<unsigned char>());
/**
* This function is similar to
* the extract_boundary_dofs()
* function but it extracts those
* degrees of freedom whose shape
* functions are nonzero on at
* least part of the selected
* boundary. For continuous
* elements, this is exactly the
* set of shape functions whose
* degrees of freedom are defined
* on boundary faces. On the
* other hand, if the finite
* element in used is a
* discontinuous element, all
* degrees of freedom are defined
* in the inside of cells and
* consequently none would be
* boundary degrees of
* freedom. Several of those
* would have shape functions
* that are nonzero on the
* boundary, however. This
* function therefore extracts
* all those for which the
* FiniteElement::has_support_on_face
* function says that it is
* nonzero on any face on one of
* the selected boundary parts.
*/
template <class DH>
static void
extract_dofs_with_support_on_boundary (const DH &dof_handler,
const std::vector<bool> &component_select,
std::vector<bool> &selected_dofs,
const std::set<unsigned char> &boundary_indicators = std::set<unsigned char>());
/**
* @name Hanging Nodes
* @{
*/
/**
* Select all dofs that will be
* constrained by interface
* constraints, i.e. all hanging
* nodes.
*
* The size of @p selected_dofs
* shall equal
* <tt>dof_handler.n_dofs()</tt>. Previous
* contents of this array or
* overwritten.
*/
template <int dim, int spacedim>
static void
extract_hanging_node_dofs (const DoFHandler<dim,spacedim> &dof_handler,
std::vector<bool> &selected_dofs);
//@}
/**
* Flag all those degrees of
* freedom which are on cells
* with the given subdomain
* id. Note that DoFs on faces
* can belong to cells with
* differing subdomain ids, so
* the sets of flagged degrees of
* freedom are not mutually
* exclusive for different
* subdomain ids.
*
* If you want to get a unique
* association of degree of freedom with
* subdomains, use the
* @p get_subdomain_association
* function.
*/
template <class DH>
static void
extract_subdomain_dofs (const DH &dof_handler,
const unsigned int subdomain_id,
std::vector<bool> &selected_dofs);
/**
* Extract a vector that represents the
* constant modes of the DoFHandler for
* the components chosen by
* <tt>component_select</tt>. The
* constant modes on a discretization are
* the null space of a Laplace operator
* on the selected components with
* Neumann boundary conditions
* applied. The null space is a necessary
* ingredient for obtaining a good AMG
* preconditioner when using the class
* TrilinosWrappers::PreconditionAMG.
* Since the ML AMG package only works on
* algebraic properties of the respective
* matrix, it has no chance to detect
* whether the matrix comes from a scalar
* or a vector valued problem. However, a
* near null space supplies exactly the
* needed information about these
* components. The null space will
* consist of as many vectors as there
* are true arguments in
* <tt>component_select</tt>, each of
* which will be one in one component and
* zero in all others. We store this
* object in a vector of vectors, where
* the outer vector is of the size of the
* number of selected components, and
* each inner vector has as many
* components as there are degrees of
* freedom in the selected
* components. Note that any matrix
* associated with this null space must
* have been constructed using the same
* <tt>component_select</tt> argument,
* since the numbering of DoFs is done
* relative to the selected dofs, not to
* all dofs.
*
* The main reason for this
* program is the use of the
* null space with the
* AMG preconditioner.
*/
template <class DH>
static void
extract_constant_modes (const DH &dof_handler,
const std::vector<bool> &component_select,
std::vector<std::vector<bool> > &constant_modes);
/**
* For each active cell of a DoFHandler
* or hp::DoFHandler, extract the active
* finite element index and fill the
* vector given as second argument. This
* vector is assumed to have as many
* entries as there are active cells.
*
* For non-hp DoFHandler objects given as
* first argument, the returned vector
* will consist of only zeros, indicating
* that all cells use the same finite
* element. For a hp::DoFHandler, the
* values may be different, though.
*/
template <class DH>
static void
get_active_fe_indices (const DH &dof_handler,
std::vector<unsigned int> &active_fe_indices);
/**
* For each DoF, return in the output
* array to which subdomain (as given by
* the <tt>cell->subdomain_id()</tt> function)
* it belongs. The output array is
* supposed to have the right size
* already when calling this function.
*
* Note that degrees of freedom
* associated with faces, edges, and
* vertices may be associated with
* multiple subdomains if they are
* sitting on partition boundaries. In
* these cases, we put them into one of
* the associated partitions in an
* undefined way. This may sometimes lead
* to different numbers of degrees of
* freedom in partitions, even if the
* number of cells is perfectly
* equidistributed. While this is
* regrettable, it is not a problem in
* practice since the number of degrees
* of freedom on partition boundaries is
* asymptotically vanishing as we refine
* the mesh as long as the number of
* partitions is kept constant.
*
* This function returns the association
* of each DoF with one subdomain. If you
* are looking for the association of
* each @em cell with a subdomain, either
* query the
* <tt>cell->subdomain_id()</tt>
* function, or use the
* <tt>GridTools::get_subdomain_association</tt>
* function.
*/
template <class DH>
static void
get_subdomain_association (const DH &dof_handler,
std::vector<unsigned int> &subdomain);
/**
* Count how many degrees of freedom are
* uniquely associated with the given
* @p subdomain index.
*
* Note that there may be rare cases
* where cells with the given @p
* subdomain index exist, but none of its
* degrees of freedom are actually
* associated with it. In that case, the
* returned value will be zero.
*
* This function will generate an
* exception if there are no cells with
* the given @p subdomain index.
*
* This function returns the number of
* DoFs associated with one subdomain. If
* you are looking for the association of
* @em cells with this subdomain, use the
* <tt>GridTools::count_cells_with_subdomain_association</tt>
* function.
*/
template <class DH>
static unsigned int
count_dofs_with_subdomain_association (const DH &dof_handler,
const unsigned int subdomain);
/**
* Similar to the previous
* function, but do not just
* return the number of degrees
* of freedom that are owned by a
* given subdomain, but return a
* set of their indices.
*/
template <class DH>
static
IndexSet
dof_indices_with_subdomain_association (const DH &dof_handler,
const unsigned int subdomain);
/**
* Count how many degrees of freedom are
* uniquely associated with the given
* @p subdomain index.
*
* This function does what the previous
* one does except that it splits the
* result among the vector components of
* the finite element in use by the
* DoFHandler object. The last argument
* (which must have a length equal to the
* number of vector components) will
* therefore store how many degrees of
* freedom of each vector component are
* associated with the given subdomain.
*/
template <class DH>
static void
count_dofs_with_subdomain_association (const DH &dof_handler,
const unsigned int subdomain,
std::vector<unsigned int> &n_dofs_on_subdomain);
/**
* Count how many degrees of
* freedom out of the total
* number belong to each
* component. If the number of
* components the finite element
* has is one (i.e. you only have
* one scalar variable), then the
* number in this component
* obviously equals the total
* number of degrees of
* freedom. Otherwise, the sum of
* the DoFs in all the components
* needs to equal the total
* number.
*
* However, the last statement
* does not hold true if the
* finite element is not
* primitive, i.e. some or all of
* its shape functions are
* non-zero in more than one
* vector component. This
* applies, for example, to the
* Nedelec or Raviart-Thomas
* elements. In this case, a
* degree of freedom is counted
* in each component in which it
* is non-zero, so that the sum
* mentioned above is greater
* than the total number of
* degrees of freedom.
*
* This behavior can be switched
* off by the optional parameter
* <tt>vector_valued_once</tt>. If
* this is <tt>true</tt>, the
* number of components of a
* nonprimitive vector valued
* element is collected only in
* the first component. All other
* components will have a count
* of zero.
*
* The additional optional
* argument @p target_component
* allows for a re-sorting and
* grouping of components. To
* this end, it contains for each
* component the component number
* it shall be counted as. Having
* the same number entered
* several times sums up several
* components as the same. One of
* the applications of this
* argument is when you want to
* form block matrices and
* vectors, but want to pack
* several components into the
* same block (for example, when
* you have @p dim velocities
* and one pressure, to put all
* velocities into one block, and
* the pressure into another).
*
* The result is returned in @p
* dofs_per_component. Note that
* the size of @p
* dofs_per_component needs to be
* enough to hold all the indices
* specified in @p
* target_component. If this is
* not the case, an assertion is
* thrown. The indices not
* targetted by target_components
* are left untouched.
*/
template <int dim, int spacedim>
static void
count_dofs_per_component (const DoFHandler<dim,spacedim>& dof_handler,
std::vector<unsigned int>& dofs_per_component,
const bool vector_valued_once = false,
std::vector<unsigned int> target_component
= std::vector<unsigned int>());
/**
* Count the degrees of freedom
* in each block. This function
* is similar to
* count_dofs_per_component(),
* with the difference that the
* counting is done by
* blocks. See @ref GlossBlock
* "blocks" in the glossary for
* details. Again the vectors are
* assumed to have the correct
* size before calling this
* function. If this is not the
* case, an assertion is thrown.
*
* This function is used in the
* step-22 and
* step-31 tutorial
* programs.
*/
template <int dim, int spacedim>
static void
count_dofs_per_block (const DoFHandler<dim,spacedim>& dof_handler,
std::vector<unsigned int>& dofs_per_block,
std::vector<unsigned int> target_block
= std::vector<unsigned int>());
/**
* @deprecated See the previous
* function with the same name
* for a description. This
* function exists for
* compatibility with older
* versions only.
*/
template <int dim, int spacedim>
static void
count_dofs_per_component (const DoFHandler<dim,spacedim>& dof_handler,
std::vector<unsigned int>& dofs_per_component,
std::vector<unsigned int> target_component);
/**
* This function can be used when
* different variables shall be
* discretized on different
* grids, where one grid is
* coarser than the other. This
* idea might seem nonsensical at
* first, but has reasonable
* applications in inverse
* (parameter estimation)
* problems, where there might
* not be enough information to
* recover the parameter on the
* same grid as the state
* variable; furthermore, the
* smoothness properties of state
* variable and parameter might
* not be too much related, so
* using different grids might be
* an alternative to using
* stronger regularization of the
* problem.
*
* The basic idea of this
* function is explained in the
* following. Let us, for
* convenience, denote by
* ``parameter grid'' the coarser
* of the two grids, and by
* ``state grid'' the finer of
* the two. We furthermore assume
* that the finer grid can be
* obtained by refinement of the
* coarser one, i.e. the fine
* grid is at least as much
* refined as the coarse grid at
* each point of the
* domain. Then, each shape
* function on the coarse grid
* can be represented as a linear
* combination of shape functions
* on the fine grid (assuming
* identical ansatz
* spaces). Thus, if we
* discretize as usual, using
* shape functions on the fine
* grid, we can consider the
* restriction that the parameter
* variable shall in fact be
* discretized by shape functions
* on the coarse grid as a
* constraint. These constraints
* are linear and happen to have
* the form managed by the
* ``ConstraintMatrix'' class.
*
* The construction of these
* constraints is done as
* follows: for each of the
* degrees of freedom (i.e. shape
* functions) on the coarse grid,
* we compute its representation
* on the fine grid, i.e. how the
* linear combination of shape
* functions on the fine grid
* looks like that resembles the
* shape function on the coarse
* grid. From this information,
* we can then compute the
* constraints which have to hold
* if a solution of a linear
* equation on the fine grid
* shall be representable on the
* coarse grid. The exact
* algorithm how these
* constraints can be computed is
* rather complicated and is best
* understood by reading the
* source code, which contains
* many comments.
*
* Before explaining the use of
* this function, we would like
* to state that the total number
* of degrees of freedom used for
* the discretization is not
* reduced by the use of this
* function, i.e. even though we
* discretize one variable on a
* coarser grid, the total number
* of degrees of freedom is that
* of the fine grid. This seems
* to be counter-productive,
* since it does not give us a
* benefit from using a coarser
* grid. The reason why it may be
* useful to choose this approach
* nonetheless is three-fold:
* first, as stated above, there
* might not be enough
* information to recover a
* parameter on a fine grid,
* i.e. we chose to discretize it
* on the coarse grid not to save
* DoFs, but for other
* reasons. Second, the
* ``ConstraintMatrix'' includes
* the constraints into the
* linear system of equations, by
* which constrained nodes become
* dummy nodes; we may therefore
* exclude them from the linear
* algebra, for example by
* sorting them to the back of
* the DoF numbers and simply
* calling the solver for the
* upper left block of the matrix
* which works on the
* non-constrained nodes only,
* thus actually realizing the
* savings in numerical effort
* from the reduced number of
* actual degrees of freedom. The
* third reason is that for some
* or other reason we have chosen
* to use two different grids, it
* may be actually quite
* difficult to write a function
* that assembles the system
* matrix for finite element
* spaces on different grids;
* using the approach of
* constraints as with this
* function allows to use
* standard techniques when
* discretizing on only one grid
* (the finer one) without having
* to take care of the fact that
* one or several of the variable
* actually belong to different
* grids.
*
* The use of this function is as
* follows: it accepts as
* parameters two DoF Handlers,
* the first of which refers to
* the coarse grid and the second
* of which is the fine grid. On
* both, a finite element is
* represented by the DoF handler
* objects, which will usually
* have several components, which
* may belong to different finite
* elements. The second and
* fourth parameter of this
* function therefore state which
* variable on the coarse grid
* shall be used to restrict the
* stated component on the fine
* grid. Of course, the finite
* elements used for the
* respective components on the
* two grids need to be the
* same. An example may clarify
* this: consider the parameter
* estimation mentioned briefly
* above; there, on the fine grid
* the whole discretization is
* done, thus the variables are
* ``u'', ``q'', and the Lagrange
* multiplier ``lambda'', which
* are discretized using
* continuous linear, piecewise
* constant discontinuous, and
* continuous linear elements,
* respectively. Only the
* parameter ``q'' shall be
* represented on the coarse
* grid, thus the DoFHandler
* object on the coarse grid
* represents only one variable,
* discretized using piecewise
* constant discontinuous
* elements. Then, the parameter
* denoting the component on the
* coarse grid would be zero (the
* only possible choice, since
* the variable on the coarse
* grid is scalar), and one on
* the fine grid (corresponding
* to the variable ``q''; zero
* would be ``u'', two would be
* ``lambda''). Furthermore, an
* object of type IntergridMap
* is needed; this could in
* principle be generated by the
* function itself from the two
* DoFHandler objects, but since
* it is probably available
* anyway in programs that use
* this function, we shall use it
* instead of re-generating
* it. Finally, the computed
* constraints are entered into a
* variable of type
* ConstraintMatrix; the
* constraints are added,
* i.e. previous contents which
* may have, for example, be
* obtained from hanging nodes,
* are not deleted, so that you
* only need one object of this
* type.
*/
template <int dim, int spacedim>
static void
compute_intergrid_constraints (const DoFHandler<dim,spacedim> &coarse_grid,
const unsigned int coarse_component,
const DoFHandler<dim,spacedim> &fine_grid,
const unsigned int fine_component,
const InterGridMap<DoFHandler<dim,spacedim> > &coarse_to_fine_grid_map,
ConstraintMatrix &constraints);
/**
* This function generates a
* matrix such that when a vector
* of data with as many elements
* as there are degrees of
* freedom of this component on
* the coarse grid is multiplied
* to this matrix, we obtain a
* vector with as many elements
* are there are global degrees
* of freedom on the fine
* grid. All the elements of the
* other components of the finite
* element fields on the fine
* grid are not touched.
*
* The output of this function is
* a compressed format that can
* be given to the @p reinit
* functions of the
* SparsityPattern ad
* SparseMatrix classes.
*/
template <int dim, int spacedim>
static void
compute_intergrid_transfer_representation (const DoFHandler<dim,spacedim> &coarse_grid,
const unsigned int coarse_component,
const DoFHandler<dim,spacedim> &fine_grid,
const unsigned int fine_component,
const InterGridMap<DoFHandler<dim,spacedim> > &coarse_to_fine_grid_map,
std::vector<std::map<unsigned int, float> > &transfer_representation);
/**
* Create a mapping from degree
* of freedom indices to the
* index of that degree of
* freedom on the boundary. After
* this operation, <tt>mapping[dof]</tt>
* gives the index of the
* degree of freedom with global
* number @p dof in the list of
* degrees of freedom on the
* boundary. If the degree of
* freedom requested is not on
* the boundary, the value of
* <tt>mapping[dof]</tt> is
* @p invalid_dof_index. This
* function is mainly used when
* setting up matrices and
* vectors on the boundary from
* the trial functions, which
* have global numbers, while the
* matrices and vectors use
* numbers of the trial functions
* local to the boundary.
*
* Prior content of @p mapping
* is deleted.
*/
template <class DH>
static void
map_dof_to_boundary_indices (const DH &dof_handler,
std::vector<unsigned int> &mapping);
/**
* Same as the previous function,
* except that only those parts
* of the boundary are considered
* for which the boundary
* indicator is listed in the
* second argument.
*
* See the general doc of this
* class for more information.
*/
template <class DH>
static void
map_dof_to_boundary_indices (const DH &dof_handler,
const std::set<unsigned char> &boundary_indicators,
std::vector<unsigned int> &mapping);
/**
* Return a list of support
* points for all the degrees of
* freedom handled by this DoF
* handler object. This function,
* of course, only works if the
* finite element object used by
* the DoF handler object
* actually provides support
* points, i.e. no edge elements
* or the like. Otherwise, an
* exception is thrown.
*
* The given array must have a
* length of as many elements as
* there are degrees of freedom.
*/
template <int dim, int spacedim>
static void
map_dofs_to_support_points (const Mapping<dim,spacedim> &mapping,
const DoFHandler<dim,spacedim> &dof_handler,
std::vector<Point<spacedim> > &support_points);
/**
* This is the opposite function
* to the one above. It generates
* a map where the keys are the
* support points of the degrees
* of freedom, while the values
* are the DoF indices.
*
* Since there is no natural
* order in the space of points
* (except for the 1d case), you
* have to provide a map with an
* explicitly specified
* comparator object. This
* function is therefore
* templatized on the comparator
* object. Previous content of
* the map object is deleted in
* this function.
*
* Just as with the function
* above, it is assumed that the
* finite element in use here
* actually supports the notion
* of support points of all its
* components.
*/
template <class DH, class Comp>
static void
map_support_points_to_dofs (const Mapping<DH::dimension, DH::space_dimension> &mapping,
const DH &dof_handler,
std::map<Point<DH::space_dimension>, unsigned int, Comp> &point_to_index_map);
/**
* Map a coupling table from the
* user friendly organization by
* components to the organization
* by blocks. Specializations of
* this function for DoFHandler
* and hp::DoFHandler are
* required due to the different
* results of their finite
* element access.
*
* The return vector will be
* initialized to the correct
* length inside this function.
*/
template <int dim, int spacedim>
static void
convert_couplings_to_blocks (const hp::DoFHandler<dim,spacedim>& dof_handler,
const Table<2, Coupling>& table_by_component,
std::vector<Table<2,Coupling> >& tables_by_block);
/**
* Make a constraint matrix for the
* constraints that result from zero
* boundary values. This function is used
* in step-36, for
* example.
*/
template <int dim, int spacedim, template <int, int> class DH>
static void
make_zero_boundary_constraints (const DH<dim,spacedim> &dof,
ConstraintMatrix &zero_boundary_constraints,
const std::vector<bool> &component_mask_=std::vector<bool>());
/**
* Map a coupling table from the
* user friendly organization by
* components to the organization
* by blocks. Specializations of
* this function for DoFHandler
* and hp::DoFHandler are
* required due to the different
* results of their finite
* element access.
*
* The return vector will be
* initialized to the correct
* length inside this function.
*/
template <int dim, int spacedim>
static void
convert_couplings_to_blocks (const DoFHandler<dim,spacedim>& dof_handler,
const Table<2, Coupling>& table_by_component,
std::vector<Table<2,Coupling> >& tables_by_block);
/**
* Given a finite element and a table how
* the vector components of it couple
* with each other, compute and return a
* table that describes how the
* individual shape functions couple with
* each other.
*/
template <int dim, int spacedim>
static
Table<2,Coupling>
dof_couplings_from_component_couplings (const FiniteElement<dim,spacedim> &fe,
const Table<2,Coupling> &component_couplings);
/**
* Exception
*/
DeclException0 (ExcFEHasNoSupportPoints);
/**
* Exception
*/
DeclException0 (ExcFENotPrimitive);
/**
* Exception
*/
DeclException2 (ExcWrongSize,
int, int,
<< "The dimension " << arg1 << " of the vector is wrong. "
<< "It should be " << arg2);
/**
* Exception
*/
DeclException2 (ExcInvalidComponent,
int, int,
<< "The component you gave (" << arg1 << ") "
<< "is invalid with respect to the number "
<< "of components in the finite element "
<< "(" << arg2 << ")");
/**
* Exception
*/
DeclException0 (ExcFiniteElementsDontMatch);
/**
* Exception
*/
DeclException0 (ExcGridNotCoarser);
/**
* Exception
*/
DeclException0 (ExcGridsDontMatch);
/**
* Exception
*/
DeclException0 (ExcNoFESelected);
/**
* Exception
*/
DeclException0 (ExcInvalidBoundaryIndicator);
};
/* ------------------------- explicit specializations -------------- */
template <>
void
DoFTools::map_dof_to_boundary_indices (const DoFHandler<1,1> &dof_handler,
std::vector<unsigned int> &mapping);
/* ------------------------- inline functions -------------- */
/**
* Operator computing the maximum coupling out of two.
*
* @relates DoFTools
*/
inline
DoFTools::Coupling operator |= (DoFTools::Coupling& c1,
const DoFTools::Coupling c2)
{
if (c2 == DoFTools::always)
c1 = DoFTools::always;
else if (c1 != DoFTools::always && c2 == DoFTools::nonzero)
return c1 = DoFTools::nonzero;
return c1;
}
/**
* Operator computing the maximum coupling out of two.
*
* @relates DoFTools
*/
inline
DoFTools::Coupling operator | (const DoFTools::Coupling c1,
const DoFTools::Coupling c2)
{
if (c1 == DoFTools::always || c2 == DoFTools::always)
return DoFTools::always;
if (c1 == DoFTools::nonzero || c2 == DoFTools::nonzero)
return DoFTools::nonzero;
return DoFTools::none;
}
// ---------------------- inline and template functions --------------------
template <int dim, int spacedim>
inline unsigned int
DoFTools::max_dofs_per_cell (const DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().dofs_per_cell;
}
template <int dim, int spacedim>
inline unsigned int
DoFTools::max_dofs_per_face (const DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().dofs_per_face;
}
template <int dim, int spacedim>
inline unsigned int
DoFTools::max_dofs_per_vertex (const DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().dofs_per_vertex;
}
template <int dim, int spacedim>
inline unsigned int
DoFTools::n_components (const DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().n_components();
}
template <int dim, int spacedim>
inline unsigned int
DoFTools::fe_is_primitive (const DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().is_primitive();
}
template <int dim, int spacedim>
inline unsigned int
DoFTools::max_dofs_per_cell (const hp::DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().max_dofs_per_cell ();
}
template <int dim, int spacedim>
inline unsigned int
DoFTools::max_dofs_per_face (const hp::DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().max_dofs_per_face ();
}
template <int dim, int spacedim>
inline unsigned int
DoFTools::max_dofs_per_vertex (const hp::DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().max_dofs_per_vertex ();
}
template <int dim, int spacedim>
inline unsigned int
DoFTools::n_components (const hp::DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe()[0].n_components();
}
template <int dim, int spacedim>
inline unsigned int
DoFTools::fe_is_primitive (const hp::DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe()[0].is_primitive();
}
template <class DH, class SparsityPattern>
inline
void
DoFTools::make_sparsity_pattern (const DH &dof,
const std::vector<std::vector<bool> > &mask,
SparsityPattern &sparsity_pattern)
{
const unsigned int ncomp = dof.get_fe().n_components();
Assert (mask.size() == ncomp,
ExcDimensionMismatch(mask.size(), ncomp));
for (unsigned int i=0; i<mask.size(); ++i)
Assert (mask[i].size() == ncomp,
ExcDimensionMismatch(mask[i].size(), ncomp));
// Create a coupling table out of the mask
Table<2,DoFTools::Coupling> couplings(ncomp, ncomp);
for (unsigned int i=0;i<ncomp;++i)
for (unsigned int j=0;j<ncomp;++j)
if (mask[i][j])
couplings(i,j) = always;
else
couplings(i,j) = none;
// Call the new function
make_sparsity_pattern(dof, couplings, sparsity_pattern);
}
template <class DH, class Comp>
void
DoFTools::map_support_points_to_dofs (
const Mapping<DH::dimension,DH::space_dimension> &mapping,
const DH &dof_handler,
std::map<Point<DH::space_dimension>, unsigned int, Comp> &point_to_index_map)
{
// let the checking of arguments be
// done by the function first
// called
std::vector<Point<DH::space_dimension> > support_points (dof_handler.n_dofs());
map_dofs_to_support_points (mapping, dof_handler, support_points);
// now copy over the results of the
// previous function into the
// output arg
point_to_index_map.clear ();
for (unsigned int i=0; i<dof_handler.n_dofs(); ++i)
point_to_index_map[support_points[i]] = i;
}
DEAL_II_NAMESPACE_CLOSE
#endif
|