
ℋmatrix approximability of inverses of FEM matrices for the timeharmonic Maxwell equations
The inverse of the stiffness matrix of the timeharmonic Maxwell equatio...
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Stability implies robust convergence of a class of diagonalizationbased iterative algorithms
Solving wave equations in a timeparallel manner is challenging, and the...
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IMEX Parareal Integrators
Parareal is a widely studied parallelintime method that can achieve me...
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NearField Linear Sampling Method forAxisymmetric Eddy Current Tomography
This paper is concerned with EddyCurrent (EC) nondestructive testing of...
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Comparison Theorems for Splittings of Mmatrices in (block) Hessenberg Form
Some variants of the (block) GaussSeidel iteration for the solution of ...
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On the Scalability of the Parallel Schwarz Method in OneDimension
In contrast with classical Schwarz theory, recent results in computation...
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Unfolding by Folding: a resampling approach to the problem of matrix inversion without actually inverting any matrix
Matrix inversion problems are often encountered in experimental physics,...
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Analysis of parallel Schwarz algorithms for timeharmonic problems using block Toeplitz matrices
In this work we study the convergence properties of the onelevel parallel Schwarz method applied to the onedimensional and twodimensional Helmholtz and Maxwell's equations. Onelevel methods are not scalable in general. However, it has recently been proven that when impedance transmission conditions are used in the case of the algorithm applied to the equations with absorption, under certain assumptions, scalability can be achieved and no coarse space is required. We show here that this result is also true for the iterative version of the method at the continuous level for stripwise decompositions into subdomains that can typically be encountered when solving waveguide problems. The convergence proof relies on the particular block Toeplitz structure of the global iteration matrix. Although nonHermitian, we prove that its limiting spectrum has a near identical form to that of a Hermitian matrix of the same structure. We illustrate our results with numerical experiments.
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