1! 2! Description: Solves a nonlinear system in parallel with SNES. 3! We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular 4! domain, using distributed arrays (DMDAs) to partition the parallel grid. 5! The command line options include: 6! -par <parameter>, where <parameter> indicates the nonlinearity of the problem 7! problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81) 8! 9 10! 11! -------------------------------------------------------------------------- 12! 13! Solid Fuel Ignition (SFI) problem. This problem is modeled by 14! the partial differential equation 15! 16! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1, 17! 18! with boundary conditions 19! 20! u = 0 for x = 0, x = 1, y = 0, y = 1. 21! 22! A finite difference approximation with the usual 5-point stencil 23! is used to discretize the boundary value problem to obtain a nonlinear 24! system of equations. 25! 26! The uniprocessor version of this code is snes/tutorials/ex4f.F 27! 28! -------------------------------------------------------------------------- 29! The following define must be used before including any PETSc include files 30! into a module or interface. This is because they can't handle declarations 31! in them 32! 33 34 module ex5f90module 35#include <petsc/finclude/petscsnes.h> 36#include <petsc/finclude/petscdmda.h> 37 use petscsnes 38 use petscdmda 39 type userctx 40 PetscInt xs,xe,xm,gxs,gxe,gxm 41 PetscInt ys,ye,ym,gys,gye,gym 42 PetscInt mx,my 43 PetscMPIInt rank 44 PetscReal lambda 45 end type userctx 46 47 contains 48! --------------------------------------------------------------------- 49! 50! FormFunction - Evaluates nonlinear function, F(x). 51! 52! Input Parameters: 53! snes - the SNES context 54! X - input vector 55! dummy - optional user-defined context, as set by SNESSetFunction() 56! (not used here) 57! 58! Output Parameter: 59! F - function vector 60! 61! Notes: 62! This routine serves as a wrapper for the lower-level routine 63! "FormFunctionLocal", where the actual computations are 64! done using the standard Fortran style of treating the local 65! vector data as a multidimensional array over the local mesh. 66! This routine merely handles ghost point scatters and accesses 67! the local vector data via VecGetArray() and VecRestoreArray(). 68! 69 subroutine FormFunction(snes,X,F,user,ierr) 70 implicit none 71 72! Input/output variables: 73 SNES snes 74 Vec X,F 75 PetscErrorCode ierr 76 type (userctx) user 77 DM da 78 79! Declarations for use with local arrays: 80 PetscScalar,pointer :: lx_v(:),lf_v(:) 81 Vec localX 82 83! Scatter ghost points to local vector, using the 2-step process 84! DMGlobalToLocalBegin(), DMGlobalToLocalEnd(). 85! By placing code between these two statements, computations can 86! be done while messages are in transition. 87 PetscCall(SNESGetDM(snes,da,ierr)) 88 PetscCall(DMGetLocalVector(da,localX,ierr)) 89 PetscCall(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr)) 90 PetscCall(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr)) 91 92! Get a pointer to vector data. 93! - For default PETSc vectors, VecGetArray() returns a pointer to 94! the data array. Otherwise, the routine is implementation dependent. 95! - You MUST call VecRestoreArray() when you no longer need access to 96! the array. 97! - Note that the interface to VecGetArray() differs from VecGetArray(). 98 99 PetscCall(VecGetArray(localX,lx_v,ierr)) 100 PetscCall(VecGetArray(F,lf_v,ierr)) 101 102! Compute function over the locally owned part of the grid 103 PetscCall(FormFunctionLocal(lx_v,lf_v,user,ierr)) 104 105! Restore vectors 106 PetscCall(VecRestoreArray(localX,lx_v,ierr)) 107 PetscCall(VecRestoreArray(F,lf_v,ierr)) 108 109! Insert values into global vector 110 111 PetscCall(DMRestoreLocalVector(da,localX,ierr)) 112 PetscCall(PetscLogFlops(11.0d0*user%ym*user%xm,ierr)) 113 114! PetscCallA(VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)) 115! PetscCallA(VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)) 116 end subroutine formfunction 117 end module ex5f90module 118 119 module ex5f90moduleinterfaces 120 use ex5f90module 121 122 Interface SNESSetApplicationContext 123 Subroutine SNESSetApplicationContext(snes,ctx,ierr) 124 use ex5f90module 125 SNES snes 126 type(userctx) ctx 127 PetscErrorCode ierr 128 End Subroutine 129 End Interface SNESSetApplicationContext 130 131 Interface SNESGetApplicationContext 132 Subroutine SNESGetApplicationContext(snes,ctx,ierr) 133 use ex5f90module 134 SNES snes 135 type(userctx), pointer :: ctx 136 PetscErrorCode ierr 137 End Subroutine 138 End Interface SNESGetApplicationContext 139 end module ex5f90moduleinterfaces 140 141 program main 142 use ex5f90module 143 use ex5f90moduleinterfaces 144 implicit none 145! 146 147! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 148! Variable declarations 149! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 150! 151! Variables: 152! snes - nonlinear solver 153! x, r - solution, residual vectors 154! J - Jacobian matrix 155! its - iterations for convergence 156! Nx, Ny - number of preocessors in x- and y- directions 157! matrix_free - flag - 1 indicates matrix-free version 158! 159 SNES snes 160 Vec x,r 161 Mat J 162 PetscErrorCode ierr 163 PetscInt its 164 PetscBool flg,matrix_free 165 PetscInt ione,nfour 166 PetscReal lambda_max,lambda_min 167 type (userctx) user 168 DM da 169 170! Note: Any user-defined Fortran routines (such as FormJacobian) 171! MUST be declared as external. 172 external FormInitialGuess,FormJacobian 173 174! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 175! Initialize program 176! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 177 PetscCallA(PetscInitialize(ierr)) 178 PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)) 179 180! Initialize problem parameters 181 lambda_max = 6.81 182 lambda_min = 0.0 183 user%lambda = 6.0 184 ione = 1 185 nfour = 4 186 PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',user%lambda,flg,ierr)) 187 PetscCheckA(user%lambda .lt. lambda_max .and. user%lambda .gt. lambda_min,PETSC_COMM_SELF,PETSC_ERR_USER,'Lambda provided with -par is out of range') 188 189! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 190! Create nonlinear solver context 191! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 192 PetscCallA(SNESCreate(PETSC_COMM_WORLD,snes,ierr)) 193 194! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 195! Create vector data structures; set function evaluation routine 196! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 197 198! Create distributed array (DMDA) to manage parallel grid and vectors 199 200! This really needs only the star-type stencil, but we use the box 201! stencil temporarily. 202 PetscCallA(DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,nfour,nfour,PETSC_DECIDE,PETSC_DECIDE,ione,ione,PETSC_NULL_INTEGER_ARRAY,PETSC_NULL_INTEGER_ARRAY,da,ierr)) 203 PetscCallA(DMSetFromOptions(da,ierr)) 204 PetscCallA(DMSetUp(da,ierr)) 205 206 PetscCallA(DMDAGetInfo(da,PETSC_NULL_INTEGER,user%mx,user%my,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_DMBOUNDARYTYPE,PETSC_NULL_DMBOUNDARYTYPE,PETSC_NULL_DMBOUNDARYTYPE,PETSC_NULL_DMDASTENCILTYPE,ierr)) 207 208! 209! Visualize the distribution of the array across the processors 210! 211! PetscCallA(DMView(da,PETSC_VIEWER_DRAW_WORLD,ierr)) 212 213! Extract global and local vectors from DMDA; then duplicate for remaining 214! vectors that are the same types 215 PetscCallA(DMCreateGlobalVector(da,x,ierr)) 216 PetscCallA(VecDuplicate(x,r,ierr)) 217 218! Get local grid boundaries (for 2-dimensional DMDA) 219 PetscCallA(DMDAGetCorners(da,user%xs,user%ys,PETSC_NULL_INTEGER,user%xm,user%ym,PETSC_NULL_INTEGER,ierr)) 220 PetscCallA(DMDAGetGhostCorners(da,user%gxs,user%gys,PETSC_NULL_INTEGER,user%gxm,user%gym,PETSC_NULL_INTEGER,ierr)) 221 222! Here we shift the starting indices up by one so that we can easily 223! use the Fortran convention of 1-based indices (rather 0-based indices). 224 user%xs = user%xs+1 225 user%ys = user%ys+1 226 user%gxs = user%gxs+1 227 user%gys = user%gys+1 228 229 user%ye = user%ys+user%ym-1 230 user%xe = user%xs+user%xm-1 231 user%gye = user%gys+user%gym-1 232 user%gxe = user%gxs+user%gxm-1 233 234 PetscCallA(SNESSetApplicationContext(snes,user,ierr)) 235 236! Set function evaluation routine and vector 237 PetscCallA(SNESSetFunction(snes,r,FormFunction,user,ierr)) 238 239! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 240! Create matrix data structure; set Jacobian evaluation routine 241! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 242 243! Set Jacobian matrix data structure and default Jacobian evaluation 244! routine. User can override with: 245! -snes_fd : default finite differencing approximation of Jacobian 246! -snes_mf : matrix-free Newton-Krylov method with no preconditioning 247! (unless user explicitly sets preconditioner) 248! -snes_mf_operator : form matrix used to construct the preconditioner as set by the user, 249! but use matrix-free approx for Jacobian-vector 250! products within Newton-Krylov method 251! 252! Note: For the parallel case, vectors and matrices MUST be partitioned 253! accordingly. When using distributed arrays (DMDAs) to create vectors, 254! the DMDAs determine the problem partitioning. We must explicitly 255! specify the local matrix dimensions upon its creation for compatibility 256! with the vector distribution. Thus, the generic MatCreate() routine 257! is NOT sufficient when working with distributed arrays. 258! 259! Note: Here we only approximately preallocate storage space for the 260! Jacobian. See the users manual for a discussion of better techniques 261! for preallocating matrix memory. 262 263 PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-snes_mf',matrix_free,ierr)) 264 if (.not. matrix_free) then 265 PetscCallA(DMSetMatType(da,MATAIJ,ierr)) 266 PetscCallA(DMCreateMatrix(da,J,ierr)) 267 PetscCallA(SNESSetJacobian(snes,J,J,FormJacobian,user,ierr)) 268 endif 269 270! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 271! Customize nonlinear solver; set runtime options 272! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 273! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>) 274 PetscCallA(SNESSetDM(snes,da,ierr)) 275 PetscCallA(SNESSetFromOptions(snes,ierr)) 276 277! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 278! Evaluate initial guess; then solve nonlinear system. 279! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 280! Note: The user should initialize the vector, x, with the initial guess 281! for the nonlinear solver prior to calling SNESSolve(). In particular, 282! to employ an initial guess of zero, the user should explicitly set 283! this vector to zero by calling VecSet(). 284 285 PetscCallA(FormInitialGuess(snes,x,ierr)) 286 PetscCallA(SNESSolve(snes,PETSC_NULL_VEC,x,ierr)) 287 PetscCallA(SNESGetIterationNumber(snes,its,ierr)) 288 if (user%rank .eq. 0) then 289 write(6,100) its 290 endif 291 100 format('Number of SNES iterations = ',i5) 292 293! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 294! Free work space. All PETSc objects should be destroyed when they 295! are no longer needed. 296! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 297 if (.not. matrix_free) PetscCallA(MatDestroy(J,ierr)) 298 PetscCallA(VecDestroy(x,ierr)) 299 PetscCallA(VecDestroy(r,ierr)) 300 PetscCallA(SNESDestroy(snes,ierr)) 301 PetscCallA(DMDestroy(da,ierr)) 302 303 PetscCallA(PetscFinalize(ierr)) 304 end 305 306! --------------------------------------------------------------------- 307! 308! FormInitialGuess - Forms initial approximation. 309! 310! Input Parameters: 311! X - vector 312! 313! Output Parameter: 314! X - vector 315! 316! Notes: 317! This routine serves as a wrapper for the lower-level routine 318! "InitialGuessLocal", where the actual computations are 319! done using the standard Fortran style of treating the local 320! vector data as a multidimensional array over the local mesh. 321! This routine merely handles ghost point scatters and accesses 322! the local vector data via VecGetArray() and VecRestoreArray(). 323! 324 subroutine FormInitialGuess(snes,X,ierr) 325 use ex5f90module 326 use ex5f90moduleinterfaces 327 implicit none 328 329! Input/output variables: 330 SNES snes 331 type(userctx), pointer:: puser 332 Vec X 333 PetscErrorCode ierr 334 DM da 335 336! Declarations for use with local arrays: 337 PetscScalar,pointer :: lx_v(:) 338 339 ierr = 0 340 PetscCallA(SNESGetDM(snes,da,ierr)) 341 PetscCallA(SNESGetApplicationContext(snes,puser,ierr)) 342! Get a pointer to vector data. 343! - For default PETSc vectors, VecGetArray() returns a pointer to 344! the data array. Otherwise, the routine is implementation dependent. 345! - You MUST call VecRestoreArray() when you no longer need access to 346! the array. 347! - Note that the interface to VecGetArray() differs from VecGetArray(). 348 349 PetscCallA(VecGetArray(X,lx_v,ierr)) 350 351! Compute initial guess over the locally owned part of the grid 352 PetscCallA(InitialGuessLocal(puser,lx_v,ierr)) 353 354! Restore vector 355 PetscCallA(VecRestoreArray(X,lx_v,ierr)) 356 357! Insert values into global vector 358 359 end 360 361! --------------------------------------------------------------------- 362! 363! InitialGuessLocal - Computes initial approximation, called by 364! the higher level routine FormInitialGuess(). 365! 366! Input Parameter: 367! x - local vector data 368! 369! Output Parameters: 370! x - local vector data 371! ierr - error code 372! 373! Notes: 374! This routine uses standard Fortran-style computations over a 2-dim array. 375! 376 subroutine InitialGuessLocal(user,x,ierr) 377 use ex5f90module 378 implicit none 379 380! Input/output variables: 381 type (userctx) user 382 PetscScalar x(user%xs:user%xe,user%ys:user%ye) 383 PetscErrorCode ierr 384 385! Local variables: 386 PetscInt i,j 387 PetscReal temp1,temp,hx,hy 388 PetscReal one 389 390! Set parameters 391 392 ierr = 0 393 one = 1.0 394 hx = one/(user%mx-1) 395 hy = one/(user%my-1) 396 temp1 = user%lambda/(user%lambda + one) 397 398 do 20 j=user%ys,user%ye 399 temp = min(j-1,user%my-j)*hy 400 do 10 i=user%xs,user%xe 401 if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then 402 x(i,j) = 0.0 403 else 404 x(i,j) = temp1 * sqrt(min(hx*min(i-1,user%mx-i),temp)) 405 endif 406 10 continue 407 20 continue 408 409 end 410 411! --------------------------------------------------------------------- 412! 413! FormFunctionLocal - Computes nonlinear function, called by 414! the higher level routine FormFunction(). 415! 416! Input Parameter: 417! x - local vector data 418! 419! Output Parameters: 420! f - local vector data, f(x) 421! ierr - error code 422! 423! Notes: 424! This routine uses standard Fortran-style computations over a 2-dim array. 425! 426 subroutine FormFunctionLocal(x,f,user,ierr) 427 use ex5f90module 428 429 implicit none 430 431! Input/output variables: 432 type (userctx) user 433 PetscScalar x(user%gxs:user%gxe,user%gys:user%gye) 434 PetscScalar f(user%xs:user%xe,user%ys:user%ye) 435 PetscErrorCode ierr 436 437! Local variables: 438 PetscScalar two,one,hx,hy,hxdhy,hydhx,sc 439 PetscScalar u,uxx,uyy 440 PetscInt i,j 441 442 one = 1.0 443 two = 2.0 444 hx = one/(user%mx-1) 445 hy = one/(user%my-1) 446 sc = hx*hy*user%lambda 447 hxdhy = hx/hy 448 hydhx = hy/hx 449 450! Compute function over the locally owned part of the grid 451 452 do 20 j=user%ys,user%ye 453 do 10 i=user%xs,user%xe 454 if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then 455 f(i,j) = x(i,j) 456 else 457 u = x(i,j) 458 uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j)) 459 uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1)) 460 f(i,j) = uxx + uyy - sc*exp(u) 461 endif 462 10 continue 463 20 continue 464 465 end 466 467! --------------------------------------------------------------------- 468! 469! FormJacobian - Evaluates Jacobian matrix. 470! 471! Input Parameters: 472! snes - the SNES context 473! x - input vector 474! dummy - optional user-defined context, as set by SNESSetJacobian() 475! (not used here) 476! 477! Output Parameters: 478! jac - Jacobian matrix 479! jac_prec - optionally different matrix used to construct the preconditioner (not used here) 480! 481! Notes: 482! This routine serves as a wrapper for the lower-level routine 483! "FormJacobianLocal", where the actual computations are 484! done using the standard Fortran style of treating the local 485! vector data as a multidimensional array over the local mesh. 486! This routine merely accesses the local vector data via 487! VecGetArray() and VecRestoreArray(). 488! 489! Notes: 490! Due to grid point reordering with DMDAs, we must always work 491! with the local grid points, and then transform them to the new 492! global numbering with the "ltog" mapping 493! We cannot work directly with the global numbers for the original 494! uniprocessor grid! 495! 496! Two methods are available for imposing this transformation 497! when setting matrix entries: 498! (A) MatSetValuesLocal(), using the local ordering (including 499! ghost points!) 500! - Set matrix entries using the local ordering 501! by calling MatSetValuesLocal() 502! (B) MatSetValues(), using the global ordering 503 504! - Set matrix entries using the global ordering by calling 505! MatSetValues() 506! Option (A) seems cleaner/easier in many cases, and is the procedure 507! used in this example. 508! 509 subroutine FormJacobian(snes,X,jac,jac_prec,user,ierr) 510 use ex5f90module 511 implicit none 512 513! Input/output variables: 514 SNES snes 515 Vec X 516 Mat jac,jac_prec 517 type(userctx) user 518 PetscErrorCode ierr 519 DM da 520 521! Declarations for use with local arrays: 522 PetscScalar,pointer :: lx_v(:) 523 Vec localX 524 525! Scatter ghost points to local vector, using the 2-step process 526! DMGlobalToLocalBegin(), DMGlobalToLocalEnd() 527! Computations can be done while messages are in transition, 528! by placing code between these two statements. 529 530 PetscCallA(SNESGetDM(snes,da,ierr)) 531 PetscCallA(DMGetLocalVector(da,localX,ierr)) 532 PetscCallA(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr)) 533 PetscCallA(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr)) 534 535! Get a pointer to vector data 536 PetscCallA(VecGetArray(localX,lx_v,ierr)) 537 538! Compute entries for the locally owned part of the Jacobian preconditioner. 539 PetscCallA(FormJacobianLocal(lx_v,jac_prec,user,ierr)) 540 541! Assemble matrix, using the 2-step process: 542! MatAssemblyBegin(), MatAssemblyEnd() 543! Computations can be done while messages are in transition, 544! by placing code between these two statements. 545 546 PetscCallA(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)) 547 if (jac .ne. jac_prec) then 548 PetscCallA(MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)) 549 endif 550 PetscCallA(VecRestoreArray(localX,lx_v,ierr)) 551 PetscCallA(DMRestoreLocalVector(da,localX,ierr)) 552 PetscCallA(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)) 553 if (jac .ne. jac_prec) then 554 PetscCallA(MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)) 555 endif 556 557! Tell the matrix we will never add a new nonzero location to the 558! matrix. If we do it will generate an error. 559 560 PetscCallA(MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr)) 561 562 end 563 564! --------------------------------------------------------------------- 565! 566! FormJacobianLocal - Computes Jacobian matrix used to compute the preconditioner, 567! called by the higher level routine FormJacobian(). 568! 569! Input Parameters: 570! x - local vector data 571! 572! Output Parameters: 573! jac_prec - Jacobian matrix used to compute the preconditioner 574! ierr - error code 575! 576! Notes: 577! This routine uses standard Fortran-style computations over a 2-dim array. 578! 579! Notes: 580! Due to grid point reordering with DMDAs, we must always work 581! with the local grid points, and then transform them to the new 582! global numbering with the "ltog" mapping 583! We cannot work directly with the global numbers for the original 584! uniprocessor grid! 585! 586! Two methods are available for imposing this transformation 587! when setting matrix entries: 588! (A) MatSetValuesLocal(), using the local ordering (including 589! ghost points!) 590! - Set matrix entries using the local ordering 591! by calling MatSetValuesLocal() 592! (B) MatSetValues(), using the global ordering 593! - Then apply this map explicitly yourself 594! - Set matrix entries using the global ordering by calling 595! MatSetValues() 596! Option (A) seems cleaner/easier in many cases, and is the procedure 597! used in this example. 598! 599 subroutine FormJacobianLocal(x,jac_prec,user,ierr) 600 use ex5f90module 601 implicit none 602 603! Input/output variables: 604 type (userctx) user 605 PetscScalar x(user%gxs:user%gxe,user%gys:user%gye) 606 Mat jac_prec 607 PetscErrorCode ierr 608 609! Local variables: 610 PetscInt row,col(5),i,j 611 PetscInt ione,ifive 612 PetscScalar two,one,hx,hy,hxdhy 613 PetscScalar hydhx,sc,v(5) 614 615! Set parameters 616 ione = 1 617 ifive = 5 618 one = 1.0 619 two = 2.0 620 hx = one/(user%mx-1) 621 hy = one/(user%my-1) 622 sc = hx*hy 623 hxdhy = hx/hy 624 hydhx = hy/hx 625 626! Compute entries for the locally owned part of the Jacobian. 627! - Currently, all PETSc parallel matrix formats are partitioned by 628! contiguous chunks of rows across the processors. 629! - Each processor needs to insert only elements that it owns 630! locally (but any non-local elements will be sent to the 631! appropriate processor during matrix assembly). 632! - Here, we set all entries for a particular row at once. 633! - We can set matrix entries either using either 634! MatSetValuesLocal() or MatSetValues(), as discussed above. 635! - Note that MatSetValues() uses 0-based row and column numbers 636! in Fortran as well as in C. 637 638 do 20 j=user%ys,user%ye 639 row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1 640 do 10 i=user%xs,user%xe 641 row = row + 1 642! boundary points 643 if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then 644 col(1) = row 645 v(1) = one 646 PetscCallA(MatSetValuesLocal(jac_prec,ione,[row],ione,col,v,INSERT_VALUES,ierr)) 647! interior grid points 648 else 649 v(1) = -hxdhy 650 v(2) = -hydhx 651 v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i,j)) 652 v(4) = -hydhx 653 v(5) = -hxdhy 654 col(1) = row - user%gxm 655 col(2) = row - 1 656 col(3) = row 657 col(4) = row + 1 658 col(5) = row + user%gxm 659 PetscCallA(MatSetValuesLocal(jac_prec,ione,[row],ifive,col,v,INSERT_VALUES,ierr)) 660 endif 661 10 continue 662 20 continue 663 664 end 665 666! 667!/*TEST 668! 669! test: 670! nsize: 4 671! args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always 672! requires: !single 673! 674! test: 675! suffix: 2 676! nsize: 4 677! args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always 678! requires: !single 679! 680! test: 681! suffix: 3 682! nsize: 3 683! args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always 684! requires: !single 685! 686! test: 687! suffix: 4 688! nsize: 3 689! args: -snes_mf_operator -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always 690! requires: !single 691! 692! test: 693! suffix: 5 694! requires: !single 695! 696!TEST*/ 697