<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=""><br class=""></div> You can use MatCreateMFFD <a href="https://petsc.org/main/docs/manualpages/Mat/MatCreateMFFD/" class="">https://petsc.org/main/docs/manualpages/Mat/MatCreateMFFD/</a> MatMFFDSetFunction MatSetFromOptions MatMFFDSetBase and provide the matrix to KSP. Note you will need to use -pc_type none or provide your own custom preconditioner with <a href="https://petsc.org/main/docs/manualpages/PC/PCSHELL/" class="">https://petsc.org/main/docs/manualpages/PC/PCSHELL/</a><div class=""><br class=""></div><div class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On May 24, 2022, at 1:21 PM, Tu, Jiannan <<a href="mailto:Jiannan_Tu@uml.edu" class="">Jiannan_Tu@uml.edu</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta charset="UTF-8" class=""><div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;">I want to use a matrix-free matrix to solve a large linear equation system because the matrix is too large to be stored. Petsc user manual describes matrix-free method for SNES with examples. The matrix-free matrices section explains how to set up such a matrix, but I can't find any example of matrix-free method with KSP. <span style="background-color: rgb(255, 255, 255); display: inline !important;" class="">I am wondering how to apply the method to KSP iterative solver in parallel.</span></div><div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;"><span style="background-color: rgb(255, 255, 255); display: inline !important;" class=""><span class=""><br class=""></span></span></div><div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;"><span style="background-color: rgb(255, 255, 255); display: inline !important;" class=""><span class="">I greatly appreciate your help for me to understand this topic. </span></span></div><div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;"><span style="background-color: rgb(255, 255, 255); display: inline !important;" class=""><span class=""><br class=""></span></span></div><div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;"><span style="background-color: rgb(255, 255, 255); display: inline !important;" class=""><span class="">Jiannan Tu</span></span></div></div></blockquote></div><br class=""></div></body></html>