Related papers: Field conserving adaptive mesh refinement (AMR) sc…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
Regularization-based image restoration has remained an active research topic in computer vision and image processing. It often leverages a guidance signal captured in different fields as an additional cue. In this work, we present a general…
This research rigorously investigates the convergence of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in elastic solids. We specifically examine a novel Ambrosio-Tortorelli (AT1)…
Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure.…
The density matrix renormalization group (DMRG) algorithm is a popular alternating minimization scheme for solving high-dimensional optimization problems in the tensor train format. Classical DMRG, however, is based on sequential…
Pixel- and voxel-based representations of microstructures obtained from tomographic imaging methods is an established standard in computational materials science. The corresponding highly resolved, uniform discretitization in numerical…
Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffusion-reaction models arise as solutions to the associated…
In this work, we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials (FGMs). A recovery type error indicator combined with quadtree decomposition is employed for adaptive…
We propose and analyze an Accelerated Rearrangement Method (ARM) for solving a class of nonconvex optimization problems involving two-phase composites. These problems include maximizing the (work) energy of a membrane governed by the…
GPUs and other accelerators are increasingly used for scientific computing. In the future, we want to add GPU support to parallel adaptive mesh refinement (AMR) codes written in Fortran. To understand which changes are necessary to obtain…
Solving large-scale nonlinear minimization problems is computationally demanding. Nonlinear multilevel minimization (NMM) methods explore the structure of the underlying minimization problem to solve such problems in a computationally…
We introduce CRASH-AMR, a new version of the cosmological Radiative Transfer (RT) code CRASH, enabled to use refined grids. This new feature allows us to attain higher resolution in our RT simulations and thus to describe more accurately…
We describe an initial implementation of an electrostatic Particle-in-Cell (ES-PIC) module with adaptive Cartesian mesh in our Unified Flow Solver framework. Challenges of PIC method with cell-based adaptive mesh refinement (AMR) are…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
Humans and animals recognize objects irrespective of the beholder's point of view, which may drastically change their appearances. Artificial pattern recognizers also strive to achieve this, e.g., through translational invariance in…
We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing…
We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…
Automatic Speech Recognition (ASR) has seen remarkable advancements with deep neural networks, such as Transformer and Conformer. However, these models typically have large model sizes and high inference costs, posing a challenge to deploy…
In this work, we present a general framework for the design and analysis of two-level AMG methods. The approach is to find a basis for locally optimal or quasi-optimal coarse space, such as the space of constant vectors for standard…
We propose an Adaptive Perfectly Matched Layer (APML) to be used in diffraction grating modeling. With a properly tailored co-ordinate stretching depending both on the incident field and on grating parameters, the APML may efficiently…