Graduate Thesis of Cristián Pérez
Program | PhD in Applied Sciences with mention in Mathematical Engineering, Universidad de Concepción | |
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Enrollment Year | 1995 | |
Senior Year | 2001 | |
Thesis Title | Methods for the Integral Frontier Equations and its Coupling with Finite Element Methods | |
Thesis Summary:In this thesis we consider the application of wavelet methods to the coupling of finite element and boundary element methods into two dimensions. By means of compression techniques of matrices by means of bases of biortogonal partitions for the boundary terms with N degrees of freedom, it is proved that the convergence of the compressed scheme is not deteriorated, whereas the number of coefficients in the corresponding stiffness matrices is Considerably smaller than N ^ 2 N. Since the coupling method deals with the Dirichlet and Neumann data, it is necessary to consider integral boundary operators of nonzero orders and Sobolev spaces of fractional orders. In this context, the bases of wavelets can be normalized to be stable in these spaces. This property, combined with the known BPX preconditioner, is used to construct a preconditioner for the complete matrix system resulting from the coupling method. | ||
Thesis Director(s) | Freddy Paiva | |
Thesis Project Approval Date | 1997, July 10 | |
Thesis Defense Date | 2001, March 30 | |
Professional Monitoring | March 2001 - March 2002: Postdoctoral Research, CCentro de Modelamiento Matematico, Universidad de Chile, Santiago, under the direction of Professor Dr. Carlos Conca. | |
PDF Thesis | Download Thesis PDF | |
ISI Publications from the ThesisHelmut HARBRECHT, Freddy PAIVA, Cristian PEREZ, Reinhold SCHNEIDER: Multiscale preconditioning for the coupling of FEM-BEM. Numerical Linear Algebra with Applications, vol. 10, 3, pp. 197-222, (2003) Helmut HARBRECHT, Freddy PAIVA, Cristian PEREZ, Reinhold SCHNEIDER: Biorthogonal wavelet approximation for the coupling of FEM-BEM. Numerische Mathematik, vol. 92, 2, pp. 325-356, (2002) |
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