<html><body><div style="font-family: arial, helvetica, sans-serif; font-size: 12pt; color: #000000"><div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;">Hello everyone,</div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;"><br></div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;">I have some questions regarding a linear system that I am solving in my plasma simulations. We have in this case a strongly non-symmetric matrix due to the cylindrical coordinates for which the Laplacian cell is given by Fig. 2 for two kinds of triangles. The different unstructured grids have from 300 000 nodes to 7 000 000 nodes.</div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;"><br></div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;">To my understanding, CG should not work properly on this matrix but BiCGStab(1) should. When using SOR preconditioner it is indeed the case: -ksp_type cg -pc_type sor yields solutions in 10 to 20 times more iterations than -ksp_type bcgs -pc_type sor.</div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;"><br></div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;">However, when switching to -ksp_type cg -pc_type gamg the convergence is great and even slightly better than -ksp_type bcgs. I do not understand how CG is able to make the system converge when using GAMG although the matrix is non-symmetric ? Is GAMG able to somehow symmetrize the system? I have the impression that when using -pc_type gamg the Krylov solver is actually the Pre-relaxation and post-relaxation of the initial grid, is that right?</div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;"><br></div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;">For GAMG since the matrix is non-symmetric -mg_levels_pc_type sor for and -mg_levels_ksp_type richardson have been used and yields better results than the original chebychev solver.</div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;"><br></div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;">Sincerely yours,</div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;"><br></div><div style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;" data-mce-style="caret-color: #000000; color: #000000; font-family: arial, helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;">Lionel Cheng</div></div></div></body></html>