<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""><br class=""></div> A side note: The <span style="font-family: Calibri, sans-serif; font-size: 11pt;" class="">MatNullSpaceTest tells you that the null space you provided is in the null space of the operator, it does not say if you have found the entire null space. In your case with two subdomains the null space is actually two dimensional; all constant on one domain (0 on the other) and 0 on the first domain and all constant on the second. So you need to pass two vectors into the MatNullSpaceCreate(). But regardless the test should work for all constant on both domains.</span><div><br class=""><blockquote type="cite" class=""><div class="">On Dec 7, 2021, at 11:19 AM, Marco Cisternino <<a href="mailto:marco.cisternino@optimad.it" class="">marco.cisternino@optimad.it</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta charset="UTF-8" class=""><div class="WordSection1" style="page: WordSection1; caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; 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;"><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Good morning,<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">I’m still struggling with the Poisson equation with Neumann BCs.<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">I discretize the equation by finite volume method and I divide every line of the linear system by the volume of the cell. I could avoid this division, but I’m trying to understand.<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">My mesh is not uniform, i.e. cells have different volumes (it is an octree mesh).<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Moreover, in my computational domain there are 2 separated sub-domains.<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">I build the null space and then I use MatNullSpaceTest to check it.<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">If I do this:<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">MatNullSpaceCreate(getCommunicator(), PETSC_TRUE, 0, nullptr, &nullspace);<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">It works<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">If I do this:<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="FR" class="">Vec nsp;<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="FR" class="">VecDuplicate(m_rhs, &nsp);<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="FR" class="">VecSet(nsp,1.0);<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="FR" class="">VecNormalize(nsp, nullptr);<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">MatNullSpaceCreate(getCommunicator(), PETSC_FALSE, 1, &nsp, &nullspace);<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">It does not work<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Probably, I have wrong expectations, but should not it be the same?<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Thanks<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span class="">Marco Cisternino, PhD<br class=""><a href="mailto:marco.cisternino@optimad.it" class=""><span style="color: blue;" class="">marco.cisternino@optimad.it</span></a><o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">______________________<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Optimad Engineering Srl<o:p class=""></o:p></span></div><div style="margin: 0cm; 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