Thesis Summary:

This Thesis is concerned with the combination of Finite Element, Boundary Element, Dirichlet to Neumann mappings and Domain Decomposition Methods for the numerical solving of linear and nonlinear exterior boundary value problems arising in Potential Theory and Elasticity. The algorithms for linear problems are based on Dirichlet to Neumann mappings to transform the exterior problem into a mixed boundary value problem on a bounded domain. This domain is decomposed into a finite number of annular nonoverlapping sub-domains which, by means of Steklov Poincaré operators, allows to obtain a symmetric interface problem. Then, this problem is solved by using iterative methods, based on Dirichlet Robin preconditioners, leading to iteration by subdomains algorithms well suited for parallel computations. In what concerning nonlinear problems, we present a linearization procedure based on linear preconditioners. As models in Potential Theory, we consider the exterior Dirichlet problem for the Laplacian in the plane and a class of nonlinear exterior strongly monotone problems. In Elasticity we consider the exterior Dirichlet problem for the Lamé system and an exterior problem in bidimensional elastoiplasticity. We discuss the variational aspects of the presented algorithms, approximation of StekloviPoincaré operators and provide the corresponding finite dimensional analysis. Also, we give some numerical experiments which confirm our results.

ISI Publications from the Thesis

Gabriel N. GATICA, George C. HSIAO, Mario E. MELLADO: A domain decomposition method based on BEM and FEM for linear exterior boundary value problems. Journal of Mathematical Analysis and Applications, vol. 262, 1, pp. 70-86, (2001)

Gabriel N. GATICA, Erwin HERNáNDEZ, Mario E. MELLADO: A domain decomposition method for linear exterior boundary value problems. Applied Mathematics Letters, vol. 11, 6, pp. 1-9, (1998)

Gabriel N. GATICA, Mario E. MELLADO: On the numerical solution of linear exterior problems via the uncoupling method. International Journal for Numerical Methods in Engineering, vol. 41, 2, pp. 233-251, (1998)

No-ISI Publications from the Thesis

Gabriel N. GATICA, Mario E. MELLADO: Nonoverlapping domain decomposition methods for linear and nonlinear exterior boundary value problems. Computational Mechanics. New trends and applications, S. Idelsohn, E. Onate, eds.,CD-ROM, Part I, Section 2, No. 26, CIMNE, Barcelona, 1998

Other Publications (ISI)

Norbert HEUER, Mario E. MELLADO, Ernst P. STEPHAN: A p-adaptive algorithm for the BEM with the hypersingular operator on the plane screen. International Journal for Numerical Methods in Engineering, vol. 53, 1, pp. 85-104, (2002)

Norbert HEUER, Mario E. MELLADO, Ernst P. STEPHAN: hp-adaptive two-level methods for boundary integral equations on curves. COMPUTING, vol. 67, 4, pp. 305-334, (2001)

Mario E. MELLADO, Rodolfo RODRíGUEZ: Efficient solution of fluid-structure vibration problems. Applied Numerical Mathematics, vol. 36, 4, pp. 389-400, (2001)