
Bayesian inversion for electromyography using lowrank tensor formats
The reconstruction of the structure of biological tissue using electromy...
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Lowrank tensor methods for Markov chains with applications to tumor progression models
Continuoustime Markov chains describing interacting processes exhibit a...
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A Lowrank Method for Parameterdependent Fluidstructure Interaction Discretizations With Hyperelasticity
In aerospace engineering and boat building, fluidstructure interaction ...
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Lowrank representation of tensor network operators with longrange pairwise interactions
Tensor network operators, such as the matrix product operator (MPO) and ...
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A Lowrank Approach for Nonlinear Parameterdependent Fluidstructure Interaction Problems
Parameterdependent discretizations of linear fluidstructure interactio...
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TensorKrylov method for computing eigenvalues of parameterdependent matrices
In this paper we extend the Residual Arnoldi method for calculating an e...
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Adaptive force biasing algorithms: new convergence results and tensor approximations of the bias
A modification of the Adaptive Biasing Force method is introduced, in wh...
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A parameterdependent smoother for the multigrid method
The solution of parameterdependent linear systems, by classical methods, leads to an arithmetic effort that grows exponentially in the number of parameters. This renders the multigrid method, which has a well understood convergence theory, infeasible. A parameterdependent representation, e.g., a lowrank tensor format, can avoid this exponential dependence, but in these it is unknown how to calculate the inverse directly within the representation. The combination of these representations with the multigrid method requires a parameterdependent version of the classical multigrid theory and a parameterdependent representation of the linear system, the smoother, the prolongation and the restriction. A derived parameterdependent version of the smoothing property, fulfilled by parameterdependent versions of the Richardson and Jacobi methods, together with the approximation property prove the convergence of the multigrid method for arbitrary parameterdependent representations. For a model problem lowrank tensor formats represent the parameterdependent linear system, prolongation and restriction. The smoother, a damped Jacobi method, is directly approximated in the lowrank tensor format by using exponential sums. Proving the smoothing property for this approximation guarantees the convergence of the parameterdependent method. Numerical experiments for the parameterdependent model problem, with bounded parameter value range, indicate a grid size independent convergence rate.
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