Related papers: Testing a new mesh refinement code in the evolutio…
Computationally solving the equations of elasticity is a key component in many materials science and mechanics simulations. Phenomena such as deformation-induced microstructure evolution, microfracture, and microvoid nucleation are examples…
In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…
We propose a new splitting method for strong numerical solution of the Cox-Ingersoll-Ross model. For this method, applied over both deterministic and adaptive random meshes, we prove a uniform moment bound and strong error results of order…
This work is devoted to the numerical simulation of nonlinear Schr\"odinger and Klein-Gordon equations. We present a general strategy to construct numerical schemes which are uniformly accurate with respect to the oscillation frequency.…
We propose a new algorithm for Adaptive Finite Element Methods (AFEMs) based on smoothing iterations (S-AFEM), for linear, second-order, elliptic partial differential equations (PDEs). The algorithm is inspired by the ascending phase of the…
The Douglas--Rachford (DR) and alternating direction method of multipliers (ADMM) are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to…
Many solid mechanics problems on complex geometries are conventionally solved using discrete boundary methods. However, such an approach can be cumbersome for problems involving evolving domain boundaries due to the need to track boundaries…
Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. We present a new method for implicit adaptive time-stepping on adaptive mesh refinement-grids. We…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
We extend the entropy-stable oscillation-eliminating discontinuous Galerkin spectral element method (ES-OEDG) on curvilinear meshes to adaptive mesh refinement (AMR) grids with nonconforming interfaces. The formulation targets…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
For computational acoustics, schemes need to have low-dispersion and low-dissipation properties in order to capture the amplitude and phase of the wave correctly. To improve the spectral properties of the scheme, the authors have previously…
Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence…
Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable parameters and/or ingredients. Paradigmatic examples include the…
Adaptive mesh refinement (AMR) reduces computational costs in CFD by concentrating resolution where needed, but efficiently embedding complex, non-aligned geometries on GPUs remains challenging. We present a GPU-native algorithm for…
Matching information across image and text modalities is a fundamental challenge for many applications that involve both vision and natural language processing. The objective is to find efficient similarity metrics to compare the similarity…
Population imaging studies rely upon good quality medical imagery before downstream image quantification. This study provides an automated approach to assess image quality from cardiovascular magnetic resonance (CMR) imaging at scale. We…
In this paper, we implement the Adaptive Moving Mesh method (AMM) to the solution of initial value problems involving the Schr\"odinger equation, and more specifically the Schr\"odinger-Poisson system of equations. This method is based on…
We study the evolution of solidification microstructures using a phase-field model computed on an adaptive, finite element grid. We discuss the details of our algorithm and show that it greatly reduces the computational cost of solving the…
We explore the problem of approximate matrix multiplication (AMM) within the sliding window model, where algorithms utilize limited space to perform large-scale matrix multiplication in a streaming manner. This model has garnered increasing…