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- Bängtsson, Erik, et al.
(författare)
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A comparison between two solution techniques to solve the equations of linear isostasy
- 2006
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we compare two models to compute the isostatic response of the Earths lithosphere to an external load. The lithosphere is modeled as a linear elastic solid. The two models differ in the mathematical formulation of the problem, their applicability in the incompressible limit, the choice of the finite elements used for discretization, and the solution strategy for the arising algebraic problem. The efficiency and accuracy of both models are compared via extensive numerical experiments in 2D and 3D.
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- Bängtsson, Erik
(författare)
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A consistent stabilized formulation for a nonsymmetric saddle-point problem
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this report we study the stability of a nonsymmetric saddle-point problem. It is discretized with equal order finite elements and stabilized with a consistent regularization. In this way we achieve a stable finite element discretization of optimal order approximation properties.
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- Bängtsson, Erik, et al.
(författare)
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Approaches to Reduce the Computational Cost when Solving Linear Systems of Equations Arising in Boundary Element Method Discretizations
- 2003
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Preconditioned iterative solution methods are compared with the direct Gaussian elimination method to solve dense linear systems Ax = b which originate from crack propagation problems, modeled and discretized by boundary element (BEM) techniques.Numerical experiments are presented and compared with the direct solution method available in a commercial BEM package. The experiments show that the preconditioned iterative schemes are competitive compared to the direct solver with respect to both arithmetic operations required and memory demands.
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- Bängtsson, Erik, et al.
(författare)
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Finite element block-factorized preconditioners
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this work we consider block-factorized preconditioners for the iterative solution of systems of linear algebraic equations arising from finite element discretizations of scalar and vector partial differential equations of elliptic type.For the construction of the preconditioners we utilize a general two-level standard finite element framework and the corresponding block two-by-two form of the system matrix, induced by a splitting of the finite element spaces, referred to as fine and coarse, namely, A = begin{bmatrix} A11&A12\ A21&A22end{bmatrix} \beginmatrixfine,\ coarse.end{matrix} . The matrix A admits the exact factorization A = \beginbmatrixA11&0\ A21&SAend{bmatrix} \beginbmatrixI1&A11-1A12\ 0& I2end{bmatrix} , where SA=A22-A21A11-1A12 and I1, I2 are identity matrices of corresponding size. The particular form of preconditioners we analyze here is MB = \beginbmatrixB11&0\ A21&Send{bmatrix} \beginbmatrixI1&Z12\ 0& I2end{bmatrix} , where S is assumed to be some available good quality approximation of the Schur complement matrix SA. We propose two methods to construct an efficient, sparse and computationally cheap approximation B11-1 of the inverse of the pivot block A11-1, required when solving systems with the block factorized preconditioner MB. Furthermore, we propose an approximation Z12 of the off-diagonal matrix block product A11-1A12, which further reduces the computational complexity of the preconditioning step. All three approximations are based on element-by-element manipulations of local finite element matrices.The approach is applicable for both selfadjoint and non-selfadjoint problems, in two as well as in three dimensions. We analyze in detail the 2D case and provide extensive numerical evidence for the efficiency of the proposed matrix approximations.
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