<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> I tried your code but it appears the ./gyroid_solution.txt contains a vector of all zeros. Is this intended?<div class=""><br class=""></div><div class=""> Actually VecDuplicateVecs() does not copy the values in the vector so your nsp[0] will contain the zero vector anyways.</div><div class=""><br class=""></div><div class=""> Would you be able to send the data that indicates what rows of the vector are associated with each subdomain? For example a vector with all 1s on the first domain and all 2s on the second domain? I think with this one should be able to construct the 2 dimensional null space.</div><div class=""><br class=""></div><div class=""> Barry</div><div class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Dec 16, 2021, at 11:09 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="">Hello Matthew,<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">as promised I prepared a minimal (112960 rows. I’m not able to produce anything smaller than this and triggering the issue) example of the behavior I was talking about some days ago.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">What I did is to produce matrix, right hand side and initial solution of the linear system.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">As I told you before, this linear system is the discretization of the pressure equation of a predictor-corrector method for NS equations in the framework of finite volume method.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">This case has homogeneous Neumann boundary conditions. Computational domain has two independent and separated sub-domains.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">I discretize the weak formulation and I divide every row of the linear system by the volume of the relative cell.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">The underlying mesh is not uniform, therefore cells have different volumes.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">The issue I’m going to explain does not show up if the mesh is uniform, same volume for all the cells.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">I usually build the null space sub-domain by sub-domain with<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-indent: 36pt;" class="">MatNullSpaceCreate(getCommunicator(), PETSC_FALSE, nConstants, constants, &nullspace);<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Where nConstants = 2 and constants contains two normalized arrays with constant values on degrees of freedom relative to the associated sub-domain and zeros elsewhere.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">However, as a test I tried the constant over the whole domain using 2 alternatives that should produce the same null space:<o:p class=""></o:p></div><ol start="1" type="1" style="margin-bottom: 0cm; margin-top: 0cm;" class=""><li class="MsoListParagraph" style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">MatNullSpaceCreate(getCommunicator(), PETSC_TRUE, 0, nullptr, &nullspace);<o:p class=""></o:p></li><li class="MsoListParagraph" style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">Vec* nsp;<o:p class=""></o:p></li></ol><div style="margin: 0cm 0cm 0cm 36pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">VecDuplicateVecs(solution, 1, &nsp);<o:p class=""></o:p></div><div style="margin: 0cm 0cm 0cm 36pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">VecSet(nsp[0],1.0);<o:p class=""></o:p></div><div style="margin: 0cm 0cm 0cm 36pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">VecNormalize(nsp[0], nullptr);<o:p class=""></o:p></div><div style="margin: 0cm 0cm 0cm 36pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">MatNullSpaceCreate(getCommunicator(), PETSC_FALSE, 1, nsp, &nullspace);<o:p class=""></o:p></div><div style="margin: 0cm 0cm 0cm 36pt; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class="">Once I created the null space I test it using:<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify; text-indent: 36pt;" class=""><span lang="IT" class="">MatNullSpaceTest(nullspace, m_A, &isNullSpaceValid);<o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class=""><span lang="IT" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class="">The case 1 pass the test while case 2 don’t.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class=""><o:p class=""> </o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class="">I have a small code for matrix loading, null spaces creation and testing.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class="">Unfortunately I cannot implement a small code able to produce that linear system.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class=""><o:p class=""> </o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class="">As attachment you can find an archive containing the matrix, the initial solution (used to manually build the null space) and the rhs (not used in the test code) in binary format.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class="">You can also find the testing code in the same archive.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class="">I used petsc 3.12(gcc+openMPI) and petsc 3.15.2(intelOneAPI) same results.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class="">If the attachment is not delivered, I can share a link to it.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class=""><o:p class=""> </o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class="">Thanks for any help.<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: justify;" class=""><o:p class=""> </o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Marco Cisternino<span class="Apple-converted-space"> </span><o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="IT" class="">Marco Cisternino, PhD<br class=""><a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class="">marco.cisternino@optimad.it</a><o:p class=""></o:p></span></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">______________________<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Optimad Engineering Srl<o:p class=""></o:p></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Via Bligny 5,<span class="Apple-converted-space"> </span><span style="font-family: "Segoe UI", sans-serif; color: rgb(32, 31, 30); background-color: white;" class="">Torino, Italia.</span><span style="font-family: "Segoe UI", sans-serif; color: rgb(32, 31, 30);" class=""><br class=""><span style="background-color: white;" class="">+3901119719782</span><br class=""></span><span lang="IT" class=""><a href="http://www.optimad.it/" target="_blank" style="color: blue; text-decoration: underline;" class=""><span lang="EN-US" style="font-family: "Segoe UI", sans-serif; border: 1pt none windowtext; padding: 0cm; background-color: white;" class="">www.optimad.it</span></a></span><o:p class=""></o:p></div></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div class=""><div style="border-style: solid none none; border-top-width: 1pt; border-top-color: rgb(225, 225, 225); padding: 3pt 0cm 0cm;" class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><b class="">From:</b><span class="Apple-converted-space"> </span>Marco Cisternino <<a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class="">marco.cisternino@optimad.it</a>><span class="Apple-converted-space"> </span><br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>martedì 7 dicembre 2021 19:36<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span>Matthew Knepley <<a href="mailto:knepley@gmail.com" style="color: blue; text-decoration: underline;" class="">knepley@gmail.com</a>><br class=""><b class="">Cc:</b><span class="Apple-converted-space"> </span>petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;" class="">petsc-users@mcs.anl.gov</a>><br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [petsc-users] Nullspaces<o:p class=""></o:p></div></div></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;" class=""><span style="color: rgb(33, 33, 33);" class="">I will, as soon as possible...<o:p class=""></o:p></span></div></div><div id="ms-outlook-mobile-signature" class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Scarica<span class="Apple-converted-space"> </span><a href="https://aka.ms/AAb9ysg" style="color: blue; text-decoration: underline;" class="">Outlook per Android</a><o:p class=""></o:p></div></div><div class="MsoNormal" align="center" style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; text-align: center;"><hr size="2" width="98%" align="center" class=""></div><div id="divRplyFwdMsg" class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><b class=""><span style="" class="">From:</span></b><span style="" class=""><span class="Apple-converted-space"> </span>Matthew Knepley <<a href="mailto:knepley@gmail.com" style="color: blue; text-decoration: underline;" class="">knepley@gmail.com</a>><br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>Tuesday, December 7, 2021 7:25:43 PM<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span>Marco Cisternino <<a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class="">marco.cisternino@optimad.it</a>><br class=""><b class="">Cc:</b><span class="Apple-converted-space"> </span>petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;" class="">petsc-users@mcs.anl.gov</a>><br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [petsc-users] Nullspaces</span><o:p class=""></o:p></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> <o:p class=""></o:p></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">On Tue, Dec 7, 2021 at 11:19 AM Marco Cisternino <<a href="mailto:marco.cisternino@optimad.it" style="color: blue; text-decoration: underline;" class="">marco.cisternino@optimad.it</a>> wrote:<o:p class=""></o:p></div></div><div class=""><blockquote style="border-style: none none none solid; border-left-width: 1pt; border-left-color: rgb(204, 204, 204); padding: 0cm 0cm 0cm 6pt; margin-left: 4.8pt; margin-right: 0cm;" class=""><div class=""><div class=""><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="IT" class="">Good morning,<o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">I’m still struggling with the Poisson equation with Neumann BCs.</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><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.</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">My mesh is not uniform, i.e. cells have different volumes (it is an octree mesh).</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">Moreover, in my computational domain there are 2 separated sub-domains.</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">I build the null space and then I use MatNullSpaceTest to check it.</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class=""> </span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">If I do this:</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">MatNullSpaceCreate(getCommunicator(), PETSC_TRUE, 0, nullptr, &nullspace);</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">It works</span><span lang="IT" class=""><o:p class=""></o:p></span></p></div></div></blockquote><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">This produces the normalized constant vector.<o:p class=""></o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> <o:p class=""></o:p></div></div><blockquote style="border-style: none none none solid; border-left-width: 1pt; border-left-color: rgb(204, 204, 204); padding: 0cm 0cm 0cm 6pt; margin-left: 4.8pt; margin-right: 0cm;" class=""><div class=""><div class=""><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">If I do this:</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="FR" class="">Vec nsp;</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="FR" class="">VecDuplicate(m_rhs, &nsp);</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="FR" class="">VecSet(nsp,1.0);</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="FR" class="">VecNormalize(nsp, nullptr);</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">MatNullSpaceCreate(getCommunicator(), PETSC_FALSE, 1, &nsp, &nullspace);</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">It does not work</span><span lang="IT" class=""><o:p class=""></o:p></span></p></div></div></blockquote><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">This is also the normalized constant vector.<o:p class=""></o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">So you are saying that these two vectors give different results with MatNullSpaceTest()?<o:p class=""></o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Something must be wrong in the code. Can you send a minimal example of this? I will go<o:p class=""></o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">through and debug it.<o:p class=""></o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> Thanks,<o:p class=""></o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> Matt<o:p class=""></o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> <o:p class=""></o:p></div></div><blockquote style="border-style: none none none solid; border-left-width: 1pt; border-left-color: rgb(204, 204, 204); padding: 0cm 0cm 0cm 6pt; margin-left: 4.8pt; margin-right: 0cm;" class=""><div class=""><div class=""><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">Probably, I have wrong expectations, but should not it be the same?</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class=""> </span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">Thanks</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class=""> </span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="IT" class="">Marco Cisternino, PhD<br class=""><a href="mailto:marco.cisternino@optimad.it" target="_blank" style="color: blue; text-decoration: underline;" class="">marco.cisternino@optimad.it</a><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">______________________</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">Optimad Engineering Srl</span><span lang="IT" class=""><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">Via Bligny 5,<span class="Apple-converted-space"> </span></span><span lang="EN-GB" style="font-family: "Segoe UI", sans-serif; color: rgb(32, 31, 30); background-color: white;" class="">Torino, Italia.</span><span lang="EN-GB" style="font-family: "Segoe UI", sans-serif; color: rgb(32, 31, 30);" class=""><br class=""><span style="background-color: white;" class="">+3901119719782</span><br class=""></span><span lang="IT" class=""><a href="http://www.optimad.it/" target="_blank" style="color: blue; text-decoration: underline;" class=""><span lang="EN-GB" style="font-family: "Segoe UI", sans-serif; border: 1pt none windowtext; padding: 0cm; background-color: white;" class="">www.optimad.it</span></a><o:p class=""></o:p></span></p><p class="xmsonormal" style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class=""> </span><span lang="IT" class=""><o:p class=""></o:p></span></p></div></div></blockquote></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><br clear="all" class=""><o:p class=""></o:p></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">--<span class="Apple-converted-space"> </span><o:p class=""></o:p></div><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br class="">-- Norbert Wiener<o:p class=""></o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank" style="color: blue; text-decoration: underline;" class="">https://www.cse.buffalo.edu/~knepley/</a><o:p class=""></o:p></div></div></div></div></div></div></div></div></div></div></div><span id="cid:8E807FF3-44CB-4953-A291-0E86EBE4D88E"><nullspaceTest.tar.gz></span></div></blockquote></div><br class=""></div></body></html>