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On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations (2020)
Journal Article
Dumbser, M., Fambri, F., Gaburro, E., & Reinarz, A. (2020). On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations. Journal of Computational Physics, 404, Article 109088. https://doi.org/10.1016/j.jcp.2019.109088

In this paper we propose an extension of the generalized Lagrangian multiplier method (GLM) of Munz et al. [52], [30], which was originally conceived for the numerical solution of the Maxwell and MHD equations with divergence-type involutions, to the... Read More about On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations.

ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems (2020)
Journal Article
Reinarz, A., Charrier, D. E., Bader, M., Bovard, L., Dumbser, M., Duru, K., …Weinzierl, T. (2020). ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems. Computer Physics Communications, 254, Article 107251. https://doi.org/10.1016/j.cpc.2020.107251

ExaHyPE (“An Exascale Hyperbolic PDE Engine”) is a software engine for solving systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are typically derived from the conservation laws of physics and are useful in a wi... Read More about ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems.

High-performance dune modules for solving large-scale, strongly anisotropic elliptic problems with applications to aerospace composites (2019)
Journal Article
Butler, R., Dodwell, T., Reinarz, A., Sandhu, A., Scheichl, R., & Seelinger, L. (2020). High-performance dune modules for solving large-scale, strongly anisotropic elliptic problems with applications to aerospace composites. Computer Physics Communications, 249, Article 106997. https://doi.org/10.1016/j.cpc.2019.106997

The key innovation in this paper is an open-source, high-performance iterative solver for high contrast, strongly anisotropic elliptic partial differential equations implemented within dune-pdelab. The iterative solver exploits a robust, scalable two... Read More about High-performance dune modules for solving large-scale, strongly anisotropic elliptic problems with applications to aerospace composites.

Sparse grid approximation spaces for space–time boundary integral formulations of the heat equation (2019)
Journal Article
Chernov, A., & Reinarz, A. (2019). Sparse grid approximation spaces for space–time boundary integral formulations of the heat equation. Computers and Mathematics with Applications, 78(11), 3605-3619. https://doi.org/10.1016/j.camwa.2019.06.036

The aim of this paper is to develop and analyse stable and accurate numerical approximation schemes for boundary integral formulations of the heat equation with Dirichlet boundary conditions. The accuracy of Galerkin discretisations for the resulting... Read More about Sparse grid approximation spaces for space–time boundary integral formulations of the heat equation.

A Bayesian framework for assessing the strength distribution of composite structures with random defects (2018)
Journal Article
Sandhu, A., Reinarz, A., & Dodwell, T. (2018). A Bayesian framework for assessing the strength distribution of composite structures with random defects. Composite Structures, 205, 58-68. https://doi.org/10.1016/j.compstruct.2018.08.074

This paper presents a novel stochastic framework to quantify the knock down in strength from out-of-plane wrinkles at the coupon level. The key innovation is a Markov Chain Monte Carlo algorithm which rigorously derives the stochastic distribution of... Read More about A Bayesian framework for assessing the strength distribution of composite structures with random defects.

Numerical quadrature for high-dimensional singular integrals over parallelotopes (2013)
Journal Article
Chernov, A., & Reinarz, A. (2013). Numerical quadrature for high-dimensional singular integrals over parallelotopes. Computers and Mathematics with Applications, 66(7), 1213-1231. https://doi.org/10.1016/j.camwa.2013.07.017

We introduce and analyze a family of algorithms for an efficient numerical approximation of integrals of the form I=∫C(1)∫C(2)F(x,y,y−x)dydx where C(1), C(2)are d-dimensional parallelotopes (i.e. affine images of d-hypercubes) and F has a singularity... Read More about Numerical quadrature for high-dimensional singular integrals over parallelotopes.