<html><head><meta http-equiv="Content-Type" content="text/html charset=windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;">Hi,<div><br></div><div><br></div><div>While doing multigrid it is possible to explicitly set restriction and prolongation/interpolation operators in PETSC using PCMGSetRestriction and PCMGSetInterpolation. In many cases, the restriction (R) and prolongation (P) operators are simply the transpose of each other (R=P’). </div><div><br></div><div>Yet, in certain cases, for example variable viscosity Stokes with a staggered finite difference discretization, it is advantageous if they are different (see <a href="http://arxiv.org/pdf/1308.4605.pdf">http://arxiv.org/pdf/1308.4605.pdf</a>).</div><div><br></div><div>Accordding to the Wesseling textbook, Galerkin coarsening of the fine grid matrix is defined as:</div><div><br></div><div>Acoarse = R*A*P</div><div><br></div><div>Yet, as far as I can tell, PETSc seems to implement this as:</div><div><div><br></div><div>Acoarse = R*A*R’</div></div><div><br></div><div>even in the case that R is different from P’. </div><div>Is there a way for PETSc to use the actually provided prolongation and restriction operators to compute the coarse grid approximation?</div><div><br></div><div>thanks!</div><div><br></div><div>Boris</div><div><br></div><div><br></div><div><br></div><div><br></div><div><br><div apple-content-edited="true">
<div style="color: rgb(0, 0, 0); font-family: Calibri; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div style="color: rgb(0, 0, 0); font-family: Calibri; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div style="color: rgb(0, 0, 0); font-family: Calibri; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div style="color: rgb(0, 0, 0); font-variant: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px;"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">_______________________________________________________</div><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br>Boris J.P. Kaus<br><br>Institute of Geosciences, </div><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Geocycles Research Center &<br>Center for Computational Sciences.<br>University of Mainz, Mainz, Germany<br>Office: <span class="Apple-tab-span" style="white-space: pre; "> </span>00-285<br>Tel: <span class="Apple-tab-span" style="white-space: pre; "> </span>+49.6131.392.4527<br><br><a href="http://www.geo-dynamics.eu">http://www.geo-dynamics.eu</a><br></div><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">_______________________________________________________<br><br></div></span></div></div></div></div>
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