<div><div>Nope - welcome to finite precision arithmetic. What's the condition number?</div></div><div><br><div class="gmail_quote"><div>On Tue, 11 Apr 2017 at 14:07, Kaushik Kulkarni <<a href="mailto:kaushikggg@gmail.com">kaushikggg@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="gmail_msg"><div class="gmail_default gmail_msg" style="font-family:verdana,sans-serif">But anyway since I am starting off with the exact solution itself, shouldn't the norm should be zero independent of the conditioning?<br class="gmail_msg"></div></div><div class="gmail_extra gmail_msg"><br class="gmail_msg"><div class="gmail_quote gmail_msg">On Tue, Apr 11, 2017 at 11:57 AM, Dave May <span class="gmail_msg"><<a href="mailto:dave.mayhem23@gmail.com" class="gmail_msg" target="_blank">dave.mayhem23@gmail.com</a>></span> wrote:<br class="gmail_msg"><blockquote class="gmail_quote gmail_msg" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="gmail_msg"><div class="gmail_msg"><br class="gmail_msg"></div></div><div class="gmail_msg"><br class="gmail_msg"><div class="gmail_quote gmail_msg"><span class="gmail_msg"><div class="gmail_msg">On Tue, 11 Apr 2017 at 07:28, Kaushik Kulkarni <<a href="mailto:kaushikggg@gmail.com" class="gmail_msg" target="_blank">kaushikggg@gmail.com</a>> wrote:<br class="gmail_msg"></div><blockquote class="gmail_quote gmail_msg" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">A strange behavior I am observing is:<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">Problem: I have to solve A*x=rhs, and currently I am currently trying to solve for a system where I know the exact solution. I have initialized the exact solution in the Vec x_exact.<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">MatMult(A, x_exact, dummy);// Storing the value of A*x_exact in dummy<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">VecAXPY(dummy, -1.0, rhs); // dummy = dummy -rhs<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">VecNorm(dummy, NORM_INFINITY, &norm_val); // norm_val = ||dummy||, which gives us the residual norm<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">PetscPrintf(PETSC_COMM_SELF, "Norm = %f\n", norm_val); // Printing the norm.<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">// Starting with the linear solver<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">KSPCreate(PETSC_COMM_SELF, &ksp);<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">KSPSetOperators(ksp, A, A);<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">KSPSetFromOptions(ksp);<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">KSPSolve(ksp,rhs,x_exact); // Solving the system A*x= rhs, with the given initial input x_exact. So the result will also be stored in x_exact<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">On running with -pc_type lu -pc_factor_mat_solver_package superlu -ksp_monitor I get the following output:<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">Norm = 0.000000<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">  0 KSP Residual norm 4.371606462669e+04 <br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">  1 KSP Residual norm 5.850058113796e+02 <br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">  2 KSP Residual norm 5.832677911508e+02 <br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">  3 KSP Residual norm 1.987386549571e+02 <br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">  4 KSP Residual norm 1.220006530614e+02<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">  .<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">  .<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">  .</div></div></blockquote><div class="gmail_msg"><br class="gmail_msg"></div></span><div class="gmail_msg">The default KSP is left preconditioned GMRES. Hence the above iterates report the preconditioned residual. If your operator is singular, and LU generated garbage, the preconditioned residual can be very different to the true residual.</div><div class="gmail_msg"><br class="gmail_msg"></div><div class="gmail_msg">To see the true residual, use</div><div class="gmail_msg">-ksp_monitor_true_residual</div><div class="gmail_msg"><br class="gmail_msg"></div><div class="gmail_msg">Alternatively, use a right preconditioned KSP method, e.g. </div><div class="gmail_msg">-ksp_type fgmres</div><div class="gmail_msg">(or -ksp_type gcr) </div><div class="gmail_msg">With these methods, you will see the true residual with just -ksp_monitor</div><div class="gmail_msg"><br class="gmail_msg"></div><div class="gmail_msg"><br class="gmail_msg"></div><div class="gmail_msg">Thanks</div><span class="m_727931034827516966HOEnZb gmail_msg"><font color="#888888" class="gmail_msg"><div class="gmail_msg">  Dave</div></font></span><div class="gmail_msg"><div class="m_727931034827516966h5 gmail_msg"><div class="gmail_msg"><br class="gmail_msg"></div><div class="gmail_msg"><br class="gmail_msg"></div><div class="gmail_msg"><br class="gmail_msg"></div><blockquote class="gmail_quote gmail_msg" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">Since the initial guess is the exact solution should'nt the first residual itself be zero and converge in one iteration.<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">Thanks,<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">Kaushik<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div></div><div class="gmail_extra m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="gmail_quote m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">On Tue, Apr 11, 2017 at 10:08 AM, Kaushik Kulkarni <span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><<a href="mailto:kaushikggg@gmail.com" class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" target="_blank">kaushikggg@gmail.com</a>></span> wrote:<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><blockquote class="gmail_quote m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">Thank you for the inputs. <br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">I tried Barry' s suggestion to use SuperLU, but the solution does not converge and on doing -ksp_monitor -ksp_converged_reason. I get the following error:- <br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">240 KSP Residual norm 1.722571678777e+07 <br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">Linear solve did not converge due to DIVERGED_DTOL iterations 240<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">For some reason it is diverging, although I am sure that for the given system a unique solution exists.<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">Thanks,<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="gmail_default m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="font-family:verdana,sans-serif">Kaushik<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div></div><div class="m_727931034827516966m_-8542079525893194083m_3238410208736660839HOEnZb m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083m_3238410208736660839h5 m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="gmail_extra m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="gmail_quote m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">On Tue, Apr 11, 2017 at 1:04 AM, Xiaoye S. Li <span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><<a href="mailto:xsli@lbl.gov" class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" target="_blank">xsli@lbl.gov</a>></span> wrote:<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><blockquote class="gmail_quote m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">If you need to use SuperLU_DIST, the pivoting is done statically, using maximum weighted matching, so the small diagonals are usually taken care as well. It is not as good as partial pivoting, but works most of the time.<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">Sherry<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div></div><div class="m_727931034827516966m_-8542079525893194083m_3238410208736660839m_1856045536358622159HOEnZb m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083m_3238410208736660839m_1856045536358622159h5 m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="gmail_extra m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="gmail_quote m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">On Mon, Apr 10, 2017 at 12:07 PM, Barry Smith <span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><<a href="mailto:bsmith@mcs.anl.gov" class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" target="_blank">bsmith@mcs.anl.gov</a>></span> wrote:<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><blockquote class="gmail_quote m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
   I would suggest using ./configure --download-superlu and then when running the program -pc_type lu -pc_factor_mat_solver_package superlu<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
   Note that this is SuperLU, it is not SuperLU_DIST.  Superlu uses partial pivoting for numerical stability so should be able to handle the small or zero diagonal entries.<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
    Barry<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> On Apr 10, 2017, at 1:17 PM, Kaushik Kulkarni <<a href="mailto:kaushikggg@gmail.com" class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" target="_blank">kaushikggg@gmail.com</a>> wrote:<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> Hello,<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> I am trying to solve a 2500x2500 sparse matrix. To get an idea about the matrix structure I have added a file matrix.log which contains the output of MatView() and also the output of Matview_draw in the image file.<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> From the matrix structure it can be seen that Jacobi iteration won't work and some of the diagonal entries being very low(of the order of 1E-16) LU factorization would also fail.<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> C​an someone please suggest what all could I try next, in order to make the solution converge?<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> Thanks,<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> Kaushik<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> ​<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
<span class="m_727931034827516966m_-8542079525893194083m_3238410208736660839m_1856045536358622159m_6594076061433883875HOEnZb m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><font class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" color="#888888">> --<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> Kaushik Kulkarni<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> Fourth Year Undergraduate<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> Department of Mechanical Engineering<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> Indian Institute of Technology Bombay<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> Mumbai, India<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> <a href="https://kaushikcfd.github.io/About/" rel="noreferrer" class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" target="_blank">https://kaushikcfd.github.io/About/</a><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> <a href="tel:%2B91-9967687150" value="+919967687150" class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" target="_blank">+91-9967687150</a><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
> <matrix.log><<a href="http://matrix_pattern.pn" class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" target="_blank">matrix_pattern.pn</a>g><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
<br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">
</font></span></blockquote></div><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"></div>
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87150</div></div></div></div></div></span></div></div></span></div></div></span></span></font></div></div></div></div></div></div></div></div></div></div></span></div></div></div></div></span></div></div></span></div></div></span></span></font></div></div></div></div></div></div></div></div></span></div></div></div></div></span></div></div></span></div></div></span></div></div></div></div></div></div></span></div></div></div></div></span></div></div></span></div></div></span></div></div></div></div></div></div></div></div></span></div></div></div></div></span></div></div></span></div></div></span></span></font></span></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
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</div></div></blockquote></div><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" clear="all"><br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg">-- <br class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083m_3238410208736660839gmail_signature m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" data-smartmail="gmail_signature"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><span style="color:rgb(153,153,153)" class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><font class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg" size="1"><span style="font-family:monospace,monospace" class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><span class="m_727931034827516966m_-8542079525893194083gmail_msg gmail_msg"><div class="m_72793103482751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v></div></div></span></div></div></span></div></div></span></span></font></div></div></div></div></div></div></div></div></div></div></span></div></div></div></div></span></div></div></span></div></div></span></span></font></div></div></div></div></div></div></div></div></span></div></div></div></div></span></div></div></span></div></div></span></div></div></div></div></div></div></span></div></div></div></div></span></div></div></span></div></div></span></div></div></div></div></div></div></div></div></span></div></div></div></div></span></div></div></span></div></div></span></span></font></span></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
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</blockquote></div><br class="gmail_msg"><br clear="all" class="gmail_msg"><br class="gmail_msg">-- <br class="gmail_msg"><div class="m_727931034827516966gmail_signature gmail_msg" data-smartmail="gmail_signature"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span style="color:rgb(153,153,153)" class="gmail_msg"><font size="1" class="gmail_msg"><span style="font-family:monospace,monospace" class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><font size="1" class="gmail_msg"><span style="font-family:monospace,monospace" class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><font size="1" class="gmail_msg"><span style="font-family:monospace,monospace" class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><span class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg"><div class="gmail_msg">Kaushik Kulkarni<br class="gmail_msg">Fourth Year Undergraduate</div><div class="gmail_msg">Department of Mechanical Engineering<br class="gmail_msg">Indian Institute of Technology Bombay</div><div class="gmail_msg">Mumbai, India<br class="gmail_msg"><a href="https://kaushikcfd.github.io/About/" class="gmail_msg" target="_blank">https://kaushikcfd.github.io/About/</a><br class="gmail_msg"></div><div class="gmail_msg">+91-9967687150</div></div></div></div></div></span></div></div></span></div></div></span></span></font></div></div></div></div></div></div></div></div></div></div></span></div></div></div></div></span></div></div></span></div></div></span></span></font></div></div></div></div></div></div></div></div></span></div></div></div></div></span></div></div></span></div></div></span></div></div></div></div></div></div></span></div></div></div></div></span></div></div></span></div></div></span></div></div></div></div></div></div></div></div></span></div></div></div></div></span></div></div></span></div></div></span></span></font></span></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
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