Efficient preconditioning of hp-FEM matrices arising from time-varying problems: an application to topology optimization

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We generalize and provide a linear algebra-based perspective on a finite element (FE) ho-mogenization scheme, pioneered by Schneider et al. (2017)[1] and Leuschner and Fritzen (2018)[2]. The efficiency of the scheme is based on a preconditioned, well-scale ...

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The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...

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Two-level domain decomposition methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level preconditioner (or its corr ...

This paper is concerned with the asymptotic optimality of spectral coarse spaces for two-level iterative methods. Spectral coarse spaces, namely coarse spaces obtained as the span of the slowest modes of the used one-level smoother, are known to be very ef ...

We present the construction of additive multilevel preconditioners, also known as BPX preconditioners, for the solution of the linear system arising in isogeometric adaptive schemes with (truncated) hierarchical B-splines. We show that the locality of hier ...

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Inverse reconstruction from images is a central problem in many scientific and engineering disciplines. Recent progress on differentiable rendering has led to methods that can efficiently differentiate the full process of image formation with respect to mi ...

The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property th ...

Multiscale problems, such as modelling flows through porous media or predicting the mechanical properties of composite materials, are of great interest in many scientific areas. Analytical models describing these phenomena are rarely available, and one mus ...

Strong gravitational lensing is a powerful probe of cosmology and the dark matter distribution. Efficient lensing software is already a necessity to fully use its potential and the performance demands will only increase with the upcoming generation of tele ...

We introduce a two-level preconditioner for the efficient solution of large scale saddle point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (M ...

Density, speed and energy efficiency of integrated circuits have been increasing exponentially for the last four decades following Moore's law. However, power and reliability pose several challenges to the future of technology scaling. Approximate computin ...

The multiquery solution of parametric partial differential equations (PDEs), that is, PDEs depending on a vector of parameters, is computationally challenging and appears in several engineering contexts, such as PDE-constrained optimization, uncertainty qu ...

Efficient preconditioning of hp-FEM matrices arising from time-varying problems: an application to topology optimization

Chattez avec Graph Search

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Preconditioning techniques for generalized Sylvester matrix equations

Preconditioners for robust optimal control problems under uncertainty

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Mixed-precision explicit stabilized Runge-Kutta methods for single- and multi-scale differential equations

Spectral Coarse Spaces for the Substructured Parallel Schwarz Method

TimeEvolver: A program for time evolution with improved error bound

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Substructured Two-grid and Multi-grid Domain Decomposition Methods

On the asymptotic optimality of spectral coarse spaces

BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

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Novel corrector problems with exponential decay of the resonance error for numerical homogenization

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Multi space reduced basis preconditioners for parametrized Stokes equations

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Multi space reduced basis preconditioners for parametrized partial differential equations