Related papers: A versatile FEM framework with native GPU scalabil…
We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…
Recent progress in artificial intelligence (AI) and high-performance computing (HPC) have brought potentially game-changing opportunities in accelerating reactive flow simulations. In this study, we introduce an open-source computational…
We present an accurate, efficient and massively parallel finite-element code, DFT-FE, for large-scale ab-initio calculations (reaching $\sim 100,000$ electrons) using Kohn-Sham density functional theory (DFT). DFT-FE is based on a local…
Artificial Intelligence (AI) applications, such as Large Language Models, are primarily driven and executed by Graphics Processing Units (GPUs). These GPU programs (kernels) consume substantial amounts of energy, yet software developers…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex,…
Analytical framework for predicting General Matrix Multiplication (GEMM) performance on modern GPUs, focusing on runtime, power consumption, and energy efficiency. Our study employs two approaches: a custom-implemented tiled matrix…
The widespread success of foundation models in natural language processing and computer vision has inspired researchers to extend the concept to scientific machine learning and computational science. However, this position paper argues that…
We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free…
Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and…
Automatic Differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions.…
Multiphysics problems such as multicomponent diffusion, phase transformations in multiphase systems and alloy solidification involve numerical solution of a coupled system of nonlinear partial differential equations (PDEs). Numerical…
The growing complexity and scale of scientific workflows in high performance computing (HPC) environments have led to significant challenges in managing energy consumption without compromising computational performance. Traditional…
In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using…
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain).…
This work presents an enhanced Computational Analytical Micromechanics (CAM) framework for the analysis of linear thermoelastic composite materials (CMs) with random microstructure. The proposed approach is grounded in an exact Additive…
In this paper, we introduce Active Learning framework in Federated Learning for Target Domain Generalisation, harnessing the strength from both learning paradigms. Our framework, FEDALV, composed of Active Learning (AL) and Federated Domain…
We present a unified algorithmic framework for the numerical solution, constrained optimization, and physics-informed learning of PDEs with a variational structure. Our framework is based on a Galerkin discretization of the underlying…
In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced-order methods are demanded. Combining these…
This document summarizes the main concepts of the finite element (FE) theory and constitutive relations as implemented in the open-source code phase-field multiphysics materials simulator PHIMATS https://github.com/ahcomat/PHIMATS. PHIMATS…