Sparse matricies for differential methods, dense ones for integrals. Filling the matrix is a matter of calculating the coupling coefficients between elements based on the mathematical kernel for the physics under evaluation (look up Green's functions); usually simple for differential formulations, rather more complicated for integrals. Often the hardest part is getting a good mesh over the objects of interest.
There are probably some good references for differential formulations, but I'm more familiar with integrals. Specifically electromagnetics, which is probably not what you're interested in since this is an audio forum, but you'll find general integral equation stuff by searching for the method of moments.
There are probably some good references for differential formulations, but I'm more familiar with integrals. Specifically electromagnetics, which is probably not what you're interested in since this is an audio forum, but you'll find general integral equation stuff by searching for the method of moments.
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