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  1. <html>
    2. 

  2. <title>KSP</title><body bgcolor="FFFFFF">
    3. 

  3.    <div id="version" align=right><b>petsc-3.3-p3 2012-08-29</b></div>
    4. 

  4. <h2>KSP</h2>
    5. 

  5. <menu>
    6. 

  6. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex1.c.html"><CONCEPT>solving a system of linear equations</CONCEPT></A>
    7. 

  7. <menu>
    8. 

  8. Solves a tridiagonal linear system with KSP.<BR></menu>
    9. 

  9. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex12.c.html"><CONCEPT>solving a system of linear equations</CONCEPT></A>
    10. 

  10. <menu>
    11. 

  11. Solves a linear system in parallel with KSP.<BR>Input parameters include:<BR>
    12. 

  12.   -m &lt;mesh_x&gt;       : number of mesh points in x-direction<BR>
    13. 

  13.   -n &lt;mesh_n&gt;       : number of mesh points in y-direction<BR>
    14. 

  14. </menu>
    15. 

  15. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex1f.F.html"><CONCEPT>solving a system of linear equations</CONCEPT></A>
    16. 

  16. <menu>
    17. 

  17. <BR>
    18. 

  18.    Description: Solves a tridiagonal linear system with KSP.<BR>
    19. 

  19. <BR>
    20. 

  20. </menu>
    21. 

  21. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex29.c.html"><CONCEPT>solving a system of linear equations</CONCEPT></A>
    22. 

  22. <menu>
    23. 

  23. Solves 2D inhomogeneous Laplacian using multigrid.<BR></menu>
    24. 

  24. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex31.c.html"><CONCEPT>solving a system of linear equations</CONCEPT></A>
    25. 

  25. <menu>
    26. 

  26. Solves 2D compressible Euler using multigrid.<BR></menu>
    27. 

  27. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex32.c.html"><CONCEPT>solving a system of linear equations</CONCEPT></A>
    28. 

  28. <menu>
    29. 

  29. Solves 2D inhomogeneous Laplacian using multigrid.<BR></menu>
    30. 

  30. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex34.c.html"><CONCEPT>solving a system of linear equations</CONCEPT></A>
    31. 

  31. <menu>
    32. 

  32. Solves 3D Laplacian using multigrid.<BR></menu>
    33. 

  33. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex54f.F.html"><CONCEPT>solving a system of linear equations</CONCEPT></A>
    34. 

  34. <menu>
    35. 

  35. <BR>
    36. 

  36.    Description: Solve Ax=b.  A comes from an anisotropic 2D thermal problem with Q1 FEM on domain (-1,1)^2.<BR>
    37. 

  37.        Material conductivity given by tensor:<BR>
    38. 

  38.            <BR>
    39. 

  39.        D = | 1 0       |<BR>
    40. 

  40.            | 0 epsilon |<BR>
    41. 

  41. <BR>
    42. 

  42.     rotated by angle 'theta' (-theta &lt;90&gt; in degrees) with anisotropic parameter 'epsilon' (-epsilon &lt;0.0&gt;).<BR>
    43. 

  43.     Blob right hand side centered at C (-blob_center C(1),C(2) &lt;0,0&gt;)<BR>
    44. 

  44.     Dirichlet BCs on y=-1 face.<BR>
    45. 

  45. <BR>
    46. 

  46.     -out_matlab will generate binary files for A,x,b and a ex54f.m file that reads them and plots them in matlab.<BR>
    47. 

  47. <BR>
    48. 

  48.     User can change anisotropic shape with function ex54_psi().  Negative theta will switch to a circular anisotropy.<BR>
    49. 

  49. <BR>
    50. 

  50. </menu>
    51. 

  51. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex58.c.html"><CONCEPT>solving a system of linear equations</CONCEPT></A>
    52. 

  52. <menu>
    53. 

  53. Solves a tridiagonal linear system with KSP.<BR></menu>
    54. 

  54. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex2.c.html"><CONCEPT>basic parallel example;</CONCEPT></A>
    55. 

  55. <menu>
    56. 

  56. Solves a linear system in parallel with KSP.<BR>Input parameters include:<BR>
    57. 

  57.   -random_exact_sol : use a random exact solution vector<BR>
    58. 

  58.   -view_exact_sol   : write exact solution vector to stdout<BR>
    59. 

  59.   -m &lt;mesh_x&gt;       : number of mesh points in x-direction<BR>
    60. 

  60.   -n &lt;mesh_n&gt;       : number of mesh points in y-direction<BR>
    61. 

  61. </menu>
    62. 

  62. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex23.c.html"><CONCEPT>basic parallel example;</CONCEPT></A>
    63. 

  63. <menu>
    64. 

  64. Solves a tridiagonal linear system.<BR></menu>
    65. 

  65. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex46.c.html"><CONCEPT>basic parallel example;</CONCEPT></A>
    66. 

  66. <menu>
    67. 

  67. Solves a linear system in parallel with KSP and DM.<BR>Compare this to ex2 which solves the same problem without a DM.<BR>
    68. 

  68. </menu>
    69. 

  69. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex12.c.html"><CONCEPT>Laplacian, 2d</CONCEPT></A>
    70. 

  70. <menu>
    71. 

  71. Solves a linear system in parallel with KSP.<BR>Input parameters include:<BR>
    72. 

  72.   -m &lt;mesh_x&gt;       : number of mesh points in x-direction<BR>
    73. 

  73.   -n &lt;mesh_n&gt;       : number of mesh points in y-direction<BR>
    74. 

  74. </menu>
    75. 

  75. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex13.c.html"><CONCEPT>Laplacian, 2d</CONCEPT></A>
    76. 

  76. <menu>
    77. 

  77. Solves a variable Poisson problem with KSP.<BR></menu>
    78. 

  78. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex13f90.F.html"><CONCEPT>Laplacian, 2d</CONCEPT></A>
    79. 

  79. <menu>
    80. 

  80. <BR>
    81. 

  81. <BR>
    82. 

  82. </menu>
    83. 

  83. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex16.c.html"><CONCEPT>Laplacian, 2d</CONCEPT></A>
    84. 

  84. <menu>
    85. 

  85. Solves a sequence of linear systems with different right-hand-side vectors.<BR>Input parameters include:<BR>
    86. 

  86.   -ntimes &lt;ntimes&gt;  : number of linear systems to solve<BR>
    87. 

  87.   -view_exact_sol   : write exact solution vector to stdout<BR>
    88. 

  88.   -m &lt;mesh_x&gt;       : number of mesh points in x-direction<BR>
    89. 

  89.   -n &lt;mesh_n&gt;       : number of mesh points in y-direction<BR>
    90. 

  90. </menu>
    91. 

  91. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex2.c.html"><CONCEPT>Laplacian, 2d</CONCEPT></A>
    92. 

  92. <menu>
    93. 

  93. Solves a linear system in parallel with KSP.<BR>Input parameters include:<BR>
    94. 

  94.   -random_exact_sol : use a random exact solution vector<BR>
    95. 

  95.   -view_exact_sol   : write exact solution vector to stdout<BR>
    96. 

  96.   -m &lt;mesh_x&gt;       : number of mesh points in x-direction<BR>
    97. 

  97.   -n &lt;mesh_n&gt;       : number of mesh points in y-direction<BR>
    98. 

  98. </menu>
    99. 

  99. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex29.c.html"><CONCEPT>Laplacian, 2d</CONCEPT></A>
    100. 

  100. <menu>
    101. 

  101. Solves 2D inhomogeneous Laplacian using multigrid.<BR></menu>
    102. 

  102. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex32.c.html"><CONCEPT>Laplacian, 2d</CONCEPT></A>
    103. 

  103. <menu>
    104. 

  104. Solves 2D inhomogeneous Laplacian using multigrid.<BR></menu>
    105. 

  105. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex46.c.html"><CONCEPT>Laplacian, 2d</CONCEPT></A>
    106. 

  106. <menu>
    107. 

  107. Solves a linear system in parallel with KSP and DM.<BR>Compare this to ex2 which solves the same problem without a DM.<BR>
    108. 

  108. </menu>
    109. 

  109. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex15.c.html"><CONCEPT>basic parallel example</CONCEPT></A>
    110. 

  110. <menu>
    111. 

  111. Solves a linear system in parallel with KSP.  Also<BR>illustrates setting a user-defined shell preconditioner and using the<BR>
    112. 

  112. macro __FUNCT__ to define routine names for use in error handling.<BR>
    113. 

  113. Input parameters include:<BR>
    114. 

  114.   -user_defined_pc : Activate a user-defined preconditioner<BR>
    115. 

  115. </menu>
    116. 

  116. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex15f.F.html"><CONCEPT>basic parallel example</CONCEPT></A>
    117. 

  117. <menu>
    118. 

  118. <BR>
    119. 

  119.    Solves a linear system in parallel with KSP.  Also indicates<BR>
    120. 

  120.    use of a user-provided preconditioner.  Input parameters include:<BR>
    121. 

  121.       -user_defined_pc : Activate a user-defined preconditioner<BR>
    122. 

  122. <BR>
    123. 

  123.   Program usage: mpiexec ex15f [-help] [all PETSc options]<BR>
    124. 

  124. <BR>
    125. 

  125. </menu>
    126. 

  126. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex21f.F.html"><CONCEPT>basic parallel example</CONCEPT></A>
    127. 

  127. <menu>
    128. 

  128. <BR>
    129. 

  129.    Solves a linear system in parallel with KSP.  Also indicates<BR>
    130. 

  130.    use of a user-provided preconditioner.  Input parameters include:<BR>
    131. 

  131. <BR>
    132. 

  132.   Program usage: mpiexec ex21f [-help] [all PETSc options]<BR>
    133. 

  133. <BR>
    134. 

  134. </menu>
    135. 

  135. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex2f.F.html"><CONCEPT>basic parallel example</CONCEPT></A>
    136. 

  136. <menu>
    137. 

  137. <BR>
    138. 

  138.   Description: Solves a linear system in parallel with KSP (Fortran code).<BR>
    139. 

  139.                Also shows how to set a user-defined monitoring routine.<BR>
    140. 

  140. <BR>
    141. 

  141.   Program usage: mpiexec -n &lt;procs&gt; ex2f [-help] [all PETSc options]<BR>
    142. 

  142. <BR>
    143. 

  143. </menu>
    144. 

  144. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex3.c.html"><CONCEPT>basic parallel example</CONCEPT></A>
    145. 

  145. <menu>
    146. 

  146. Solves a linear system in parallel with KSP.  The matrix<BR>uses simple bilinear elements on the unit square.  To test the parallel<BR>
    147. 

  147. matrix assembly, the matrix is intentionally laid out across processors<BR>
    148. 

  148. differently from the way it is assembled.  Input arguments are:<BR>
    149. 

  149.   -m &lt;size&gt; : problem size<BR>
    150. 

  150. </menu>
    151. 

  151. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex16.c.html"><CONCEPT>repeatedly solving linear systems;</CONCEPT></A>
    152. 

  152. <menu>
    153. 

  153. Solves a sequence of linear systems with different right-hand-side vectors.<BR>Input parameters include:<BR>
    154. 

  154.   -ntimes &lt;ntimes&gt;  : number of linear systems to solve<BR>
    155. 

  155.   -view_exact_sol   : write exact solution vector to stdout<BR>
    156. 

  156.   -m &lt;mesh_x&gt;       : number of mesh points in x-direction<BR>
    157. 

  157.   -n &lt;mesh_n&gt;       : number of mesh points in y-direction<BR>
    158. 

  158. </menu>
    159. 

  159. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex5.c.html"><CONCEPT>repeatedly solving linear systems;</CONCEPT></A>
    160. 

  160. <menu>
    161. 

  161. Solves two linear systems in parallel with KSP.  The code<BR>illustrates repeated solution of linear systems with the same preconditioner<BR>
    162. 

  162. method but different matrices (having the same nonzero structure).  The code<BR>
    163. 

  163. also uses multiple profiling stages.  Input arguments are<BR>
    164. 

  164.   -m &lt;size&gt; : problem size<BR>
    165. 

  165.   -mat_nonsym : use nonsymmetric matrix (default is symmetric)<BR>
    166. 

  166. </menu>
    167. 

  167. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex6f.F.html"><CONCEPT>repeatedly solving linear systems;</CONCEPT></A>
    168. 

  168. <menu>
    169. 

  169. <BR>
    170. 

  170.   Description: This example demonstrates repeated linear solves as<BR>
    171. 

  171.   well as the use of different preconditioner and linear system<BR>
    172. 

  172.   matrices.  This example also illustrates how to save PETSc objects<BR>
    173. 

  173.   in common blocks.<BR>
    174. 

  174. <BR>
    175. 

  175. </menu>
    176. 

  176. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex9.c.html"><CONCEPT>repeatedly solving linear systems;</CONCEPT></A>
    177. 

  177. <menu>
    178. 

  178. The solution of 2 different linear systems with different linear solvers.<BR>Also, this example illustrates the repeated<BR>
    179. 

  179. solution of linear systems, while reusing matrix, vector, and solver data<BR>
    180. 

  180. structures throughout the process.  Note the various stages of event logging.<BR>
    181. 

  181. </menu>
    182. 

  182. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex7.c.html"><CONCEPT>customizing the block Jacobi preconditioner</CONCEPT></A>
    183. 

  183. <menu>
    184. 

  184. Block Jacobi preconditioner for solving a linear system in parallel with KSP.<BR>The code indicates the<BR>
    185. 

  185. procedures for setting the particular block sizes and for using different<BR>
    186. 

  186. linear solvers on the individual blocks.<BR>
    187. 

  187. </menu>
    188. 

  188. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex8.c.html"><CONCEPT>Additive Schwarz Method (ASM) with user-defined subdomains</CONCEPT></A>
    189. 

  189. <menu>
    190. 

  190. Illustrates use of the preconditioner ASM.<BR>The Additive Schwarz Method for solving a linear system in parallel with KSP.  The<BR>
    191. 

  191. code indicates the procedure for setting user-defined subdomains.  Input<BR>
    192. 

  192. parameters include:<BR>
    193. 

  193.   -user_set_subdomain_solvers:  User explicitly sets subdomain solvers<BR>
    194. 

  194.   -user_set_subdomains:  Activate user-defined subdomains<BR>
    195. 

  195. </menu>
    196. 

  196. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex8g.c.html"><CONCEPT>Additive Schwarz Method (GASM) with user-defined subdomains</CONCEPT></A>
    197. 

  197. <menu>
    198. 

  198. Illustrates use of the preconditioner GASM.<BR>The Additive Schwarz Method for solving a linear system in parallel with KSP.  The<BR>
    199. 

  199. code indicates the procedure for setting user-defined subdomains.  Input<BR>
    200. 

  200. parameters include:<BR>
    201. 

  201.   -M:                           Number of mesh points in the x direction<BR>
    202. 

  202.   -N:                           Number of mesh points in the y direction<BR>
    203. 

  203.   -user_set_subdomain_solvers:  User explicitly sets subdomain solvers<BR>
    204. 

  204.   -user_set_subdomains:         Use the user-provided subdomain partitioning routine<BR>
    205. 

  205. With -user_set_subdomains on, the following options are meaningful:<BR>
    206. 

  206.   -Mdomains:                    Number of subdomains in the x direction <BR>
    207. 

  207.   -Ndomains:                    Number of subdomains in the y direction <BR>
    208. 

  208.   -overlap:                     Size of domain overlap in terms of the number of mesh lines in x and y<BR>
    209. 

  209. General useful options:<BR>
    210. 

  210.   -pc_gasm_print_subdomains:    Print the index sets defining the subdomains<BR>
    211. 

  211. <BR>
    212. 

  212. </menu>
    213. 

  213. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex10.c.html"><CONCEPT>solving a linear system</CONCEPT></A>
    214. 

  214. <menu>
    215. 

  215. Reads a PETSc matrix and vector from a file and solves a linear system.<BR>This version first preloads and solves a small system, then loads <BR>
    216. 

  216. another (larger) system and solves it as well.  This example illustrates<BR>
    217. 

  217. preloading of instructions with the smaller system so that more accurate<BR>
    218. 

  218. performance monitoring can be done with the larger one (that actually<BR>
    219. 

  219. is the system of interest).  See the 'Performance Hints' chapter of the<BR>
    220. 

  220. users manual for a discussion of preloading.  Input parameters include<BR>
    221. 

  221.   -f0 &lt;input_file&gt; : first file to load (small system)<BR>
    222. 

  222.   -f1 &lt;input_file&gt; : second file to load (larger system)<BR>
    223. 

  223.   -trans  : solve transpose system instead<BR>
    224. 

  224. </menu>
    225. 

  225. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex27.c.html"><CONCEPT>solving a linear system</CONCEPT></A>
    226. 

  226. <menu>
    227. 

  227. Reads a PETSc matrix and vector from a file and solves the normal equations.<BR></menu>
    228. 

  228. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex41.c.html"><CONCEPT>solving a linear system</CONCEPT></A>
    229. 

  229. <menu>
    230. 

  230. Reads a PETSc matrix and vector from a socket connection,  solves a linear system and sends the result back.<BR></menu>
    231. 

  231. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex11.c.html"><CONCEPT>solving a Helmholtz equation</CONCEPT></A>
    232. 

  232. <menu>
    233. 

  233. Solves a linear system in parallel with KSP.<BR></menu>
    234. 

  234. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex11f.F.html"><CONCEPT>solving a Helmholtz equation</CONCEPT></A>
    235. 

  235. <menu>
    236. 

  236. <BR>
    237. 

  237.   Description: Solves a complex linear system in parallel with KSP (Fortran code).<BR>
    238. 

  238. <BR>
    239. 

  239. </menu>
    240. 

  240. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex13.c.html"><CONCEPT>basic sequential example</CONCEPT></A>
    241. 

  241. <menu>
    242. 

  242. Solves a variable Poisson problem with KSP.<BR></menu>
    243. 

  243. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex13f90.F.html"><CONCEPT>basic sequential example</CONCEPT></A>
    244. 

  244. <menu>
    245. 

  245. <BR>
    246. 

  246. <BR>
    247. 

  247. </menu>
    248. 

  248. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex31.c.html"><CONCEPT>semi-implicit</CONCEPT></A>
    249. 

  249. <menu>
    250. 

  250. Solves 2D compressible Euler using multigrid.<BR></menu>
    251. 

  251. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex34.c.html"><CONCEPT>Laplacian, 3d</CONCEPT></A>
    252. 

  252. <menu>
    253. 

  253. Solves 3D Laplacian using multigrid.<BR></menu>
    254. 

  254. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex2f.F.html"><CONCEPT>setting a user-defined monitoring routine</CONCEPT></A>
    255. 

  255. <menu>
    256. 

  256. <BR>
    257. 

  257.   Description: Solves a linear system in parallel with KSP (Fortran code).<BR>
    258. 

  258.                Also shows how to set a user-defined monitoring routine.<BR>
    259. 

  259. <BR>
    260. 

  260.   Program usage: mpiexec -n &lt;procs&gt; ex2f [-help] [all PETSc options]<BR>
    261. 

  261. <BR>
    262. 

  262. </menu>
    263. 

  263. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex6f.F.html"><CONCEPT>different matrices for linear system and preconditioner;</CONCEPT></A>
    264. 

  264. <menu>
    265. 

  265. <BR>
    266. 

  266.   Description: This example demonstrates repeated linear solves as<BR>
    267. 

  267.   well as the use of different preconditioner and linear system<BR>
    268. 

  268.   matrices.  This example also illustrates how to save PETSc objects<BR>
    269. 

  269.   in common blocks.<BR>
    270. 

  270. <BR>
    271. 

  271. </menu>
    272. 

  272. <LI><A HREF="../../../src/ksp/ksp/examples/tutorials/ex14f.F.html"><CONCEPT>writing a user-defined nonlinear solver</CONCEPT></A>
    273. 

  273. <menu>
    274. 

  274. <BR>
    275. 

  275. <BR>
    276. 

  276.   Solves a nonlinear system in parallel with a user-defined<BR>
    277. 

  277.   Newton method that uses KSP to solve the linearized Newton sytems.  This solver<BR>
    278. 

  278.   is a very simplistic inexact Newton method.  The intent of this code is to<BR>
    279. 

  279.   demonstrate the repeated solution of linear sytems with the same nonzero pattern.<BR>
    280. 

  280. <BR>
    281. 

  281.   This is NOT the recommended approach for solving nonlinear problems with PETSc!<BR>
    282. 

  282.   We urge users to employ the SNES component for solving nonlinear problems whenever<BR>
    283. 

  283.   possible, as it offers many advantages over coding nonlinear solvers independently.<BR>
    284. 

  284. <BR>
    285. 

  285.   We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular<BR>
    286. 

  286.   domain, using distributed arrays (DMDAs) to partition the parallel grid.<BR>
    287. 

  287. <BR>
    288. 

  288. </menu>
    289. 

  289. </menu>
    290. 

  290. </body>
    291. 

  291. </html>
    292. 

  292.