51 citations · 71 across the 15 of their papers we have counts for
17 papers
Finite Element Convergence Analysis For Wave Equations With Time-Dependent Coefficients
Oussama Al Jarroudi, Marcus J. Grote
Error estimates are proved for finite element approximations to the solution of second-order hyperbolic partial differential equations with coefficients varying in both space and t…
Adaptive FEM with explicit time integration for the wave equation
Marcus J. Grote, Omar Lakkis, Carina S. Santos
Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time-stepping [Grote, Lakkis, Santos, 2024], we devise a spac…
A posteriori error estimates for the wave equation with mesh change in the leapfrog method
Marcus J. Grote, Omar Lakkis, Carina Santos
We derive a fully computable aposteriori error estimator for a Galerkin finite element solution of the wave equation with explicit leapfrog time-stepping. Our discrete formulation…
Explicit Local Time-Stepping for the Inhomogeneous Wave Equation with Optimal Convergence
Marcus J. Grote, Simon R. J. Michel, Stefan A. Sauter
Adaptivity and local mesh refinement are crucial for the efficient numerical simulation of wave phenomena in complex geometry. Local mesh refinement, however, can impose a tiny tim…
Explicit stabilized multirate methods for the monodomain model in cardiac electrophysiology
Giacomo Rosilho de Souza, Marcus J. Grote, Simone Pezzuto +1
Fully explicit stabilized multirate (mRKC) methods are well-suited for the numerical solution of large multiscale systems of stiff ordinary differential equations thanks to their i…
Adaptive Spectral Inversion for Inverse Medium Problems
Yannik G. Gleichmann, Marcus J. Grote
A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown contro…
Error Estimates for Adaptive Spectral Decompositions
Daniel H. Baffet, Yannik G. Gleichmann, Marcus J. Grote
Adaptive spectral (AS) decompositions associated with a piecewise constant function yield small subspaces where the characteristic functions comprising are well approximate…
A controllability method for Maxwell's equations
T. Chaumont-Frelet, M. J. Grote, S. Lanteri +1
We propose a controllability method for the numerical solution of time-harmonic Maxwell's equations in their first-order formulation. By minimizing a quadratic cost functional, whi…
Uncertainty Quantification by MLMC and Local Time-stepping For Wave Propagation
Marcus J. Grote, Simon Michel, Fabio Nobile
Because of their robustness, efficiency and non-intrusiveness, Monte Carlo methods are probably the most popular approach in uncertainty quantification to computing expected values…
Adaptive spectral decompositions for inverse medium problems
Daniel H. Baffet, Marcus J. Grote, Jet Hoe Tang
Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. S…
Explicit stabilized multirate method for stiff differential equations
Assyr Abdulle, Marcus J. Grote, Giacomo Rosilho de Souza
Stabilized Runge-Kutta methods are especially efficient for the numerical solution of large systems of stiff nonlinear differential equations because they are fully explicit. For s…
Stabilized leapfrog based local time-stepping method for the wave equation
Marcus J. Grote, Simon Michel, Stefan Sauter
Local time-stepping methods permit to overcome the severe stability constraint on explicit methods caused by local mesh refinement without sacrificing explicitness. In \cite{DiazGr…
Parallel Controllability Methods For the Helmholtz Equation
Marcus J. Grote, Frédéric Nataf, Jet Hoe Tang +1
The Helmholtz equation is notoriously difficult to solve with standard numerical methods, increasingly so, in fact, at higher frequencies. Controllability methods instead transform…
Convergence analysis of energy conserving explicit local time-stepping methods for the wave equation
Marcus J. Grote, Michaela Mehlin, Stefan Sauter
Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a sm…
Explicit local time-stepping methods for time-dependent wave propagation
Marcus Grote, Teodora Mitkova
Semi-discrete Galerkin formulations of transient wave equations, either with conforming or discontinuous Galerkin finite element discretizations, typically lead to large systems of…
High-order explicit local time-stepping methods for damped wave equations
Marcus Grote, Teodora Mitkova
Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. Local time-stepping meth…
Efficient PML for the wave equation
Marcus J. Grote, Imbo Sim
In the last decade, the perfectly matched layer (PML) approach has proved a flexible and accurate method for the simulation of waves in unbounded media. Most PML formulations, howe…