Related papers: AMReX: Block-Structured Adaptive Mesh Refinement f…
FEMPAR is an open source object oriented Fortran200X scientific software library for the high-performance scalable simulation of complex multiphysics problems governed by partial differential equations at large scales, by exploiting…
Deep surrogate models for parametric partial differential equations (PDEs) can deliver high-fidelity approximations but remain prohibitively data-hungry: training often requires thousands of fine-grid simulations, each incurring substantial…
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…
We present a new adaptive resolution technique for efficient particle-based multiscale molecular dynamics (MD) simulations. The presented approach is tailor-made for molecular systems where atomistic resolution is required only in spatially…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
This paper presents a distributed memory method for anisotropic mesh adaptation that is designed to avoid the use of collective communication and global synchronization techniques. In the presented method, meshing functionality is separated…
Analyzing the increasingly large volumes of data that are available today, possibly including the application of custom machine learning models, requires the utilization of distributed frameworks. This can result in serious productivity…
The last decade has seen applications of Adaptive Mesh Refinement (AMR) methods for a wide range of problems from space physics to cosmology. With the advent of these methods, in which space is discretized into a mesh of many individual…
We consider the problem of minimizing the sum of two convex functions: one is smooth and given by a gradient oracle, and the other is separable over blocks of coordinates and has a simple known structure over each block. We develop an…
As a general framework, Matrix Exponential Dimensionality Reduction (MEDR) deals with the small-sample-size problem that appears in linear Dimensionality Reduction (DR) algorithms. High complexity is the bottleneck in this type of DR…
We study an element agglomeration coarsening strategy that requires data redistribution at coarse levels when the number of coarse elements becomes smaller than the used computational units (cores). The overall procedure generates coarse…
This study presents constructions of the space-time Conservation Element and Solution Element (CESE) methods to accommodate adaptive unstructured quadrilateral meshes. Subsequently, a novel algorithm is devised to effectively manage the…
Reconfigurable electromagnetic structures (REMSs), such as reconfigurable reflectarrays (RRAs) or reconfigurable intelligent surfaces (RISs), hold significant potential to improve the spectral efficiency of wireless communication systems…
The cost- and memory-efficient numerical simulation of coupled volume-based multi-physics problems like flow, transport, wave propagation and others remains a challenging task with finite element method (FEM) approaches. Goal-oriented space…
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)…
In the last few decades, several novel algorithms have been designed for finding critical points on PES and the minimum energy paths connecting them. This has led to considerably improve our understanding of reaction mechanisms and kinetics…
This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…
Implicit time integration is key to robustly simulating stiff materials and large deformations, but its performance is often dominated by repeatedly solving large linear systems. Adaptive coarsening can reduce this cost by concentrating…
Neural radiance fields (NeRF) have transformed 3D reconstruction and rendering, facilitating photorealistic image synthesis from sparse viewpoints. This work introduces an explicit data reuse neural rendering (EDR-NR) architecture, which…
Transformers have improved the state-of-the-art across numerous tasks in sequence modeling. Besides the quadratic computational and memory complexity w.r.t the sequence length, the self-attention mechanism only processes information at the…