5 papers
Conservative Three-Layer Schemes for Kirchhoff-Type Equations
Felix Krumbiegel, Jemal Rogava, Andreas Rupp +1
We study a Kirchhoff-type nonlinear integro-differential equation in two spatial dimensions whose coefficients are allowed to depend on time, and we construct conservative discreti…
Enriched higher-order multiscale approaches with applications to wave propagation
Balaje Kalyanaraman, Felix Krumbiegel, Roland Maier +1
We consider the numerical solution of partial differential equations with coefficients that are strongly heterogeneous in space. We provide an overview of higher-order localized or…
Optimal higher-order convergence rates for parabolic multiscale problems
Balaje Kalyanaraman, Felix Krumbiegel, Roland Maier +1
In this paper, we introduce a higher-order multiscale method for time-dependent problems with highly oscillatory coefficients. Building on the localized orthogonal decomposition (L…
Neural numerical homogenization based on Deep Ritz corrections
Mehdi Elasmi, Felix Krumbiegel, Roland Maier
Numerical homogenization methods aim at providing appropriate coarse-scale approximations of solutions to (elliptic) partial differential equations that involve highly oscillatory…
A Higher-Order Multiscale Method for the Wave Equation
Felix Krumbiegel, Roland Maier
In this paper we propose a multiscale method for the acoustic wave equation in highly oscillatory media. We use a higher-order extension of the localized orthogonal decomposition m…