Dear Community, I have a linear system of the form
|K B| du f1 = |C D| dp f2 where K is a big m x m sparsematrix that comes from some FE discretization, B is a coupling matrix (of the form m x 4), C is of the form (4 x m) and D is 4x4. I save B and C as 4 Vecs and D as a 4x4 double array. D might be singular so at the moment I use the following schur-complement approach to solve this system 1) Calculate the vecs v1 = KSP(K,PrecK) * f1, invB = [ KSP(K, PrecK) * B[0], KSP(K, PrecK) * B[1], KSP(K, PrecK) * B[2], KSP(K, PrecK) * B[3] ] 2) Build the schurcomplement S=[C ^ K^-1 B - D] via VecDots (C ^ K^-1 B [i, j] = VecDot(C[i], invB[j]) 3) invert S (this seems to be mostly non-singular) to get dp 4) calculate du with dp So counting this, I need 5x to call KSP which can be expensive and I thought of somehow doing the Schur-Complement the other way around, however due to the (possible) singularity of D this seems like a bad idea (even using a pseudoinverse) Two things puzzle me here still A) Can this be done more efficiently? B) In case my above matrix is the Jacobian in a newton method, how do I make sure with any form of Schur Complement approach that I hit the correct residual reduction? Thanks Elias -- Dr. Elias Karabelas Universitätsassistent | PostDoc Institut für Mathematik & Wissenschaftliches Rechnen | Institute of Mathematics & Scientific Computing Universität Graz | University of Graz Heinrichstraße 36, 8010 Graz Tel.: +43/(0)316/380-8546 E-Mail: elias.karabe...@uni-graz.at Web: https://ccl.medunigraz.at Bitte denken Sie an die Umwelt, bevor Sie dieses E-Mail drucken. Danke! Please consider the environment before printing this e-mail. Thank you!
