Iterative coupling algorithms for large multidomain problems with the boundary element method

Abstract

A new parallel Robin-Robin adaptive iterative coupling algorithm with dynamic relaxation parameters is proposed for the boundary element method (BEM), and relaxation parameters are derived for other existing iterative coupling algorithms. The performances of the new algorithm and of the modified existing algorithms are investigated in terms of convergence properties with respect to the number of subdomains, mesh density, interface mesh conformity, and BEM element types. Results show that the number of subdomains and the refinement level of the mesh are the two dominant factors affecting the performances of the considered algorithms. The proposed parallel Robin-Robin algorithm shows the best overall convergence behavior for the tested large problems, thanks to its effectiveness in handling complex boundary conditions and large number of subdomains, thus resulting to be very promising for efficient parallel BEM computing and large coupling problems.Source code is available at https://github.com/BinWang0213/PyBEM2D. KEYWORDSadaptive relaxation, boundary element method, domain decomposition method, iterative coupling method Int J Numer Methods Eng. 2019;117:1-14. wileyonlinelibrary.com/journal/nme

A multi-domain direct boundary element formulation for particulate flow in microchannels

“…where the partial derivatives of space coordinates are defined as and hence the CPU time can be drastically reduced [77,78]. Furthermore, the final assembly matrix is diagonally dominant, therefore the condition numbers of the resulting matrices significantly improve [74,79,80].…”

“…Furthermore, the final assembly matrix is diagonally dominant, therefore the condition numbers of the resulting matrices significantly improve [74,79,80]. MDBEM was successfully employed for heat transfer [72,73,75,77,78,[81][82][83][84][85][86], elasticity [74,[87][88][89] and Stoke's flow [79,80,[90][91][92][93] in which some variables are eliminated and the size of the final system of equations are reduced. The selection of iterative schemes or variable condensation technique is problem specific.…”

“…The selection of iterative schemes or variable condensation technique is problem specific. For large scale problems, iterative techniques may suffer from convergence issues, and the fine tuning of convergence parameters as well as initial guesses may be required [73,78]. Condensation techniques, on the other hand, are not easy to implement on computer when the solution domain is partitioned with unstructured subdomains.…”

Discontinuous Boundary Elements for Fluid Flow Problems in Discrete Fracture Networks

“…the assembly of a large system of equations, including the compatibility conditions at the interfaces among adjacent domains, may be too computationally demanding. In previous works, parallel DDMs were developed aimed at iteratively solving a series of small dense linear subsystems, rather than a coupled large unsymmetrical sparse linear system [9,10,11,46]. In DDM, conditions at interfaces are updated at each iteration, until obtaining a solution that fits the specified compatibility condition at each interface [46].…”

“…19 are satisfied up to a given tolerance TOL, this quantity being directly associated with the mass flux balance over all intersections. The optimal relaxation parameter β k is defined as follows [46]:…”