Related papers: Adjoint Methods for Guiding Adaptive Mesh Refineme…
One difficulty in developing numerical methods for tsunami modeling is the fact that solutions contain regions where much higher resolution is required than elsewhere in the domain, particularly since the solution may contain…
Adaptive mesh refinement (AMR) is often used when solving time-dependent partial differential equations using numerical methods. It enables time-varying regions of much higher resolution, which can be used to track discontinuities in the…
An implementation of adaptive mesh refinement algorithms is presented for use with multilayer shallow water equations. Currently, adaptive mesh refinement is implemented with a single layer shallow water model in the GeoClaw framework. This…
We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations.…
Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…
In an effort to study the applicability of adaptive mesh refinement (AMR) techniques to atmospheric models an interpolation-based spectral element shallow water model on a cubed-sphere grid is compared to a block-structured finite volume…
It is well known that the quasi-optimality of the Galerkin finite element method for the Helmholtz equation is dependent on the mesh size and the wave-number. In the literature, different criteria have been proposed to ensure uniform…
Dynamic optimization is currently limited by sensitivity computations that require information from full forward and adjoint wave fields. Since the forward and adjoint solutions are computed in opposing time directions, the forward solution…
In this work we develop a high-resolution mapped-grid finite volume method code to model wave propagation in two dimensions in systems of multiple orthotropic poroelastic media and/or fluids, with curved interfaces between different media.…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…
Many geophysical flow or wave propagation problems can be modeled with two-dimensional depth-averaged equations, of which the shallow water equations are the simplest example. We describe the GeoClaw software that has been designed to solve…
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 space-time adaptive strategy which includes both time evolving…
We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…
We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…
We present an algorithm to solve the dispersive depth-averaged Serre-Green-Naghdi (SGN) equations using patch-based adaptive mesh refinement. These equations require adding additional higher derivative terms to the nonlinear shallow water…
Surface matching usually provides significant deformations that can lead to structural failure due to the lack of physical policy. In this context, partial surface matching of non-linear deformable bodies is crucial in engineering to govern…
We introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial…
Adaptive meshing includes local refinement as well as coarsening of meshes. Typically, coarsening algorithms are based on an explicit refinement history. In this work, we deal with local coarsening algorithms that build on the refinement…
This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of…