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I have a 1-dimensional P1 discontinuous Galerkin discretization of the linear advection equation with 4 cells and periodic boundaries on [-pi,+pi]. I'm comparing the results from SNESComputeJacobian with a hand-written Jacobian. Being linear,
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<div dir="ltr"><div>I have a 1-dimensional P1 discontinuous Galerkin discretization of the linear advection equation with 4 cells and periodic boundaries on [-pi,+pi]. I'm comparing the results from SNESComputeJacobian with a hand-written Jacobian. Being linear, the Jacobian should be constant/independent of the solution.</div><div><br></div><div>When I set the initial condition passed to SNESComputeJacobian as some constant, say f(x)=1 or 0, the petsc finite difference jacobian agrees with my hand coded-version. But when I pass it some non-constant value, e.g. f(x)=sin(x), something goes horribly wrong in the petsc jacobian. Implementing my own rudimentary finite difference approximation (similar to how I thought petsc computes it) it returns the correct jacobian to expected error. Any idea what could be going on?</div><div><br></div><div>Analytically computed Jacobian:</div><div> 4.44089e-16 -1.10266 0.31831 -0.0852909 0 0 -0.31831 1.18795<br> 1.10266 -4.44089e-16 -1.18795 0.31831 0 0 0.0852909 -0.31831<br> -0.31831 1.18795 4.44089e-16 -1.10266 0.31831 -0.0852909 0 0<br> 0.0852909 -0.31831 1.10266 -4.44089e-16 -1.18795 0.31831 0 0<br> 0 0 -0.31831 1.18795 4.44089e-16 -1.10266 0.31831 -0.0852909<br> 0 0 0.0852909 -0.31831 1.10266 -4.44089e-16 -1.18795 0.31831<br> 0.31831 -0.0852909 0 0 -0.31831 1.18795 4.44089e-16 -1.10266<br> -1.18795 0.31831 0 0 0.0852909 -0.31831 1.10266 -4.44089e-16<br></div><div><br></div><div><br></div><div>petsc finite difference jacobian when given f(x)=1:</div><div> 4.44089e-16 -1.10266 0.31831 -0.0852909 0 0 -0.31831 1.18795<br> 1.10266 -4.44089e-16 -1.18795 0.31831 0 0 0.0852909 -0.31831<br> -0.31831 1.18795 4.44089e-16 -1.10266 0.31831 -0.0852909 0 0<br> 0.0852909 -0.31831 1.10266 -4.44089e-16 -1.18795 0.31831 0 0<br> 0 0 -0.31831 1.18795 4.44089e-16 -1.10266 0.31831 -0.0852909<br> 0 0 0.0852909 -0.31831 1.10266 -4.44089e-16 -1.18795 0.31831<br> 0.31831 -0.0852909 0 0 -0.31831 1.18795 4.44089e-16 -1.10266<br> -1.18795 0.31831 0 0 0.0852909 -0.31831 1.10266 -4.44089e-16</div><div><br></div><div>petsc finite difference jacobian when given f(x) = sin(x):</div><div>-1.65547e+08 -3.31856e+08 -1.25427e+09 4.4844e+08 0 0 1.03206e+08 7.86375e+07<br> 9.13788e+07 1.83178e+08 6.92336e+08 -2.4753e+08 0 0 -5.69678e+07 -4.34064e+07<br> 3.7084e+07 7.43387e+07 2.80969e+08 -1.00455e+08 -5.0384e+07 -2.99747e+07 0 0<br> 3.7084e+07 7.43387e+07 2.80969e+08 -1.00455e+08 -5.0384e+07 -2.99747e+07 0 0<br> 0 0 2.80969e+08 -1.00455e+08 -5.0384e+07 -2.99747e+07 -2.31191e+07 -1.76155e+07<br> 0 0 2.80969e+08 -1.00455e+08 -5.0384e+07 -2.99747e+07 -2.31191e+07 -1.76155e+07<br> 9.13788e+07 1.83178e+08 0 0 -1.24151e+08 -7.38608e+07 -5.69678e+07 -4.34064e+07<br>-1.65547e+08 -3.31856e+08 0 0 2.24919e+08 1.3381e+08 1.03206e+08 7.86375e+07<br></div><div><br></div></div>