Parallel efficiency of a boundary integral equation method for nonlinear water waves

We describe the application of domain decomposition on a boundary integral method for the study of nonlinear surface waves on water in a test case for which the domain decomposition approach is an important tool to reduce the computational effort. An important aspect is the determination of the optimum number of domains for a given parallel architecture. Previous work on hetero- geneous clusters of workstations is extended to (dedicated) parallel platforms. For these systems a better indication of the parallel performance of the domain decomposition method is obtained because of the absence of varying speed of the processing elements

Domain decomposition methods for compressed sensing

We present several domain decomposition algorithms for sequential and parallel minimization of functionals formed by a discrepancy term with respect to data and total variation constraints. The convergence properties of the algorithms are analyzed. We provide several numerical experiments, showing the successful application of the algorithms for the restoration 1D and 2D signals in interpolation/inpainting problems respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.Comment: 4 page