Another question on 3D BEM for elastostatics. Which formulation of the BEM (collocations for displacement or traction BIE, Galerkin, Symmetric Galerkin, etc.) is the best in terms of the condition number of the resulting system of linear equations, considering exact evaluation of all the integrals? Are there any papers on this topic? Any considerations are greatly appreciated. Thanks!
I like Symmetric Galerkin approach where we do Galerkin discretization of all boundary integral operators for Laplace, Helmholtz, Helmholtz, Maxwell and Elastostatic kernels and next we do fast assembly of H-Matrix. This is clear and unified theory based on Sobolev spaces. The main books for this theory is: S. Rjasanow, O. Steinbach "The fast solution of Boundary Integral Equations", O. Steinbach "Numerical Approximation Methods for Elliptic Boundary Value Problems" and S. Sauter, C. Schwab "Boundary Element Methods".
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