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Multiscale or multiphysics partial differential equations are used to model a wide range of physical systems with various applications, e.g. from material and natural science to problems in biology or engineering. When the ratio between the smallest scale ...
We explore the use of radial basis functions (RBF) in the weighted essentially non-oscillatory (WENO) reconstruction process used to solve hyperbolic conservation laws, resulting in a numerical method of arbitrarily high order to solve problems with discon ...
Discontinuous Galerkin methods have desirable properties, which make them suitable for the com- putation of wave problems. Being parallelizable and hp-adaptive makes them attractive for the simulation of large-scale tsunami propagation. In order to retriev ...
This paper is devoted to determining a space-dependent source term in an inverse problem of the time-fractional diffusion equation. We use a fully-discrete method based on a finite difference scheme in time and a local discontinuous Galerkin method (LDG) i ...
Solar energy has seen tremendous advances in the past years. For thin film photovoltaics, which use less of the expensive semiconductor materials, insufficient light absorption can be a limiting factor. It is hoped that by using diffractive optics to impro ...
In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain ...
In this paper we discuss partial differential equations with multiple scales for which scale resolution are needed in some subregions, while a separation of scale and numerical homogenization is possible in the remaining part of the computational domain. D ...
Photoredox catalysis has been developed to achieve oxidative C-H chlorination of aromatic compounds using NaCl as the chlorine source and Na2S2O8 as the oxidant. The reactions occur at room temperature and exhibit exclusive selectivity for C(sp(2))-H bonds ...
A new multiscale method combined with model order reduction is proposed for flow problems in three-scale porous media. We derive an effective three-scale model that couples a macroscopic Darcy equation, a mesoscopic Stokes-Brinkman equation, and a microsco ...
A new numerical method based on numerical homogenization and model order reduction is introduced for the solution of multiscale inverse problems. We consider a class of elliptic problems with highly oscillatory tensors that varies on a microscopic scale. W ...