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The standard local defect correction (LDC) method has been extended to include multilevel adaptive gridding, domain decomposition, and regridding. The domain decomposition algorithm provides a natural route for parallelization by employing many small tensor-product grids, rather than a single large unstructured grid; this algorithm can greatly reduce memory… (More)

- J. H. M. ten Thije Boonkkamp, Martijn Anthonissen
- J. Sci. Comput.
- 2011

We present a new finite volume scheme for the advection-diffusion-reaction equation. The scheme is second order accurate in the grid size, both for dominant diffusion and dominant advection, and has only a three-point coupling in each spatial direction. Our scheme is based on a new integral representation for the flux of the one-dimensional… (More)

- Martijn Anthonissen, B. van't Hof, Arnold Reusken
- Computing
- 1998

We present a finite volume scheme for solving elliptic boundary value problems with solutions that have one or a few small regions with high activity. The scheme results from combining the local defect correction method (LDC), introduced in [13], with standard finite volume discretizations on a global coarse and on local fine uniform grids. The iterative… (More)

- Martijn Anthonissen, R. M. M. Mattheij, J. H. M. ten Thije Boonkkamp
- Numerische Mathematik
- 2003

The standard local defect correction (LDC) method has been extended to include multilevel adaptive gridding, domain decomposition, and regridding. The domain decomposition algorithm provides a natural route for parallelization by employing many small tensor-product grids, rather than a single large unstructured grid. The algorithm is applied to a laminar… (More)

We study a one-dimensional model describing the motion of a shape-memory alloy spring at a small characteristic time scale, called here fast-temperature-activation limit. At this level, the standard Falk's model reduces to a nonlinear elliptic partial differential equation (PDE) with Newton boundary condition. We show existence and uniqueness of a bounded… (More)

A Local Defect Correction (LDC) method for solving time-dependent partial differential equations whose solutions have highly localized properties is discussed. We present some properties of the technique. Results of numerical experiments illustrate the accuracy and the efficiency of the method.

- Marialuce Graziadei, Marialuce Valentina Graziadei, Bratislav Tasic, Irina Lioulina, Martijn Anthonissen
- 2004

Dit proefschrift is goedgekeurd door de promotoren: Acknowledgements Many people contributed, in different ways, to the realisation of the research work that resulted in this thesis. First, I would like to thank prof.dr. Robert Mattheij for the support , guidance and encouragement he offered me and for promoting the very nice and enjoyable atmosphere in the… (More)

- Martijn Anthonissen
- Int. J. Comput. Math.
- 2007

We study the efficient numerical simulation of laser surface remelting, a process to improve the surface quality of steel components. To this end we use adaptive grids, which are well-suited for problems with moving heat sources. To account for the local high activity due to the heat source, we introduce local uniform grids and couple the solutions on the… (More)

We apply the finite volume method to a spherically symmetric conservation law of advection-diffusion-reaction type. For the numerical flux we use the so-called complete flux scheme. In this scheme the flux is computed from a local boundary value problem for the complete equation, including the source term. As a result, the numerical flux is the… (More)

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