Low order elastic wave equation

[acitrain]

First order Spectral Element Method (SEM) for the second order elastic wave equation.

In this PR we propose the first version of the elastic wave solver using the SEM.

The space discretization is performed using the finite element implementation provide in GEOSX. For the time integration, we use first order central finite difference scheme.

As for the acoustic solver, we implements first order Absorbing Boundary Condition.

The source injection is done using a Ricker wavelet but the source coefficients are computed using the gradient of the basis functions and not just the basis functions evaluated at the source point. This seems to generate "unwanted" S-waves in particular when the source point is not placed at the center of the element. This behaviour is due to the numerical scheme and not to a bug inside the code.

[sframba]

This seems to generate "unwanted" S-waves in particular when the source point is not placed at the center of the element.

Could you please specify that this behavior is expected and due to the numerical scheme, not to a bug?

[CusiniM]

I am moving this out of the merge queue for now coz it seems that you are still missing an integratedTests PR. I saw there is a branch called feature/lowOrderWaveEqnKernel but I wasn't sure that was the one relative to this PR. I would also suggest to avoid merging baselines in the integratedTests repository but use a rebase instead.

[sframba]

I am moving this out of the merge queue for now coz it seems that you are still missing an integratedTests PR. I saw there is a branch called feature/lowOrderWaveEqnKernel but I wasn't sure that was the one relative to this PR. I would also suggest to avoid merging baselines in the integratedTests repository but use a rebase instead.

That is indeed the correct integrateTests branch (there is a small name mismatch). Sorry about the merge, I'll use a rebase next time!