<html><head><meta http-equiv="Content-Type" content="text/html; charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""> Saransh,</div><div class=""> </div> I've add some code for SNESSetPicard() in the PETSc branch barry/2021-05-06/add-snes-picard-mf see also http<a href="s://gitlab.com/petsc/petsc/-/merge_requests/3962" class="">s://gitlab.com/petsc/petsc/-/merge_requests/3962</a> that will make your coding much easier.<div class=""><br class=""></div><div class=""> With this branch you can provide code that computes A(x), using SNESSetPicard(). </div><div class=""><br class=""></div><div class="">1) by default it will use the defection-correction form of Picard iteration A(x^n)(x^{n+1} - x^{n}) = b - A(x^n) to solve, which can be slower than Newton </div><div class=""><br class=""></div><div class="">2) with -snes_fd_color it will compute the Jacobian via coloring using SNESComputeJacobianDefaultColor() (assuming the true Jacobian has the same sparsity structure as A). The true Jacobian is J(x^n) = A'(x^n)[x^n] - A(x^n) where A'(x^n) is the third order tensor of the derivatives of A() and A'(x^n)[x^n] is a matrix, I do not know if, in general, it has the same nonzero structure as A. (I'm lost beyond matrices :-().</div><div class=""></div><div class=""><br class=""></div><div class="">3) with -snes_mf_operator it will apply the true Jacobian matrix-free and precondition it with a preconditioner built from A(x^n) matrix, for some problems this works well. </div><div class=""><br class=""></div><div class="">4) with -snes_fd it uses SNESComputeJacobianDefault() and computes the Jacobian by finite differencing one column at a time, thus it is very slow and not useful for large problems. But useful for testing with small problems.</div><div class=""><br class=""></div><div class="">So you can provide A() and need not worrying about providing the Jacobian or even the function evaluation code. It is all taken care of by SNESSetPicard().</div><div class=""><br class=""></div><div class=""> Hope this helps,</div><div class=""><br class=""></div><div class=""> Barry</div><div class=""><br class=""></div><div class=""><div class=""><div><br class=""><blockquote type="cite" class=""><div class="">On May 6, 2021, at 1:21 PM, Matthew Knepley <<a href="mailto:knepley@gmail.com" class="">knepley@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class=""><div dir="ltr" class="">On Thu, May 6, 2021 at 2:09 PM Saransh Saxena <<a href="mailto:saransh.saxena5571@gmail.com" class="">saransh.saxena5571@gmail.com</a>> wrote:<br class=""></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr" class="">Hi,<br class=""><br class="">I am trying to incorporate newton method in solving a nonlinear FEM equation using SNES from PETSc. The overall equation is of the type A(x).x = b, where b is a vector of external loads, x is the solution field (say displacements for e.g.) and A is the combined LHS matrix derived from the discretization of weak formulation of the governing finite element equation. <br class=""><br class="">While going through the manual and examples of snes, I found that I need to define the function of residual using SNESSetFunction() and jacobian using SNESSetJacobian(). In that context I had a couple of questions :-<div class=""><br class=""></div><div class="">1. In the snes tutorials I've browsed through, the functions for computing residual passed had arguments only for x, the solution vector and f, the residual vector. Is there a way a user can pass an additional vector (b) and matrix (A) for computing the residual as well? as in my case, f = b - A(x).x<br class=""></div></div></blockquote><div class=""><br class=""></div><div class="">You would give PETSc an outer function MyResidual() that looked like this:</div><div class=""><br class=""></div><div class="">PetscErrorCode MyResidual(SNES snes, Vec X, Vec F, void *ctx)</div><div class="">{</div><div class=""> <call your code to compute b, or pass it in using ctx></div><div class=""> <call your code to compute A(X)></div><div class=""> MatMult(A, X, F);</div><div class=""> VecAXPY(F, -1.0, b);</div><div class="">}</div><div class=""> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr" class=""><div class="">2. Since computing jacobian is not that trivial, I would like to use one of the pre-built jacobian methods. Is there any other step other than setting the 3rd argument in SNESSetJacobian to SNESComputeJacobianDefault?<br class=""></div></div></blockquote><div class=""><br class=""></div><div class="">If you do nothing, we will compute it by default.</div><div class=""><br class=""></div><div class=""> Thanks,</div><div class=""><br class=""></div><div class=""> MAtt</div><div class=""> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr" class=""><div class="">Best regards,<br class=""><br class="">Saransh</div></div>
</blockquote></div><br clear="all" class=""><div class=""><br class=""></div>-- <br class=""><div dir="ltr" class="gmail_signature"><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class="">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br class="">-- Norbert Wiener</div><div class=""><br class=""></div><div class=""><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank" class="">https://www.cse.buffalo.edu/~knepley/</a><br class=""></div></div></div></div></div></div></div></div>
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