Generic domain decomposition and iterative solvers for 3D BEM problems.
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2006
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In the past two decades, considerable improvements concerning integration algorithms and solvers
involved in boundary-element formulations have been obtained. First, a great deal of efficient techniques
for evaluating singular and quasi-singular boundary-element integrals have been, definitely, established,
and second, iterative Krylov solvers have proven to be advantageous when compared to direct ones
also including non-Hermitian matrices. The former fact has implied in CPU-time reduction during
the assembling of the system of equations and the latter fact in its faster solution. In this paper, a
triangle-polar-co-ordinate transformation and the Telles co-ordinate transformation, applied in previous
works independently for evaluating singular and quasi-singular integrals, are combined to increase
the efficiency of the integration algorithms, and so, to improve the performance of the matrixassembly
routines. In addition, the Jacobi-preconditioned biconjugate gradient (J-BiCG) solver is
used to develop a generic substructuring boundary-element algorithm. In this way, it is not only the
system solution accelerated but also the computer memory optimized. Discontinuous boundary elements
are implemented to simplify the coupling algorithm for a generic number of subregions. Several
numerical experiments are carried out to show the performance of the computer code with regard to
matrix assembly and the system solving. In the discussion of results, expressed in terms of accuracy
and CPU time, advantages and potential applications of the BE code developed are highlighted.
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ARAÚJO, F. C. de; SILVA, K. I. da; TELLES, J. C. de F. Generic domain decomposition and iterative solvers for 3D BEM problems. International Journal for Numerical Methods in Engineering, v. 68, p. 448-472, 2006. Disponível em: <http://onlinelibrary.wiley.com/doi/10.1002/nme.1719/full>. Acesso em: 20 jul. 2017.