Related papers: A versatile FEM framework with native GPU scalabil…
This study introduces the concept of finite element network analysis (FENA) which is a physics-informed, machine-learning-based, computational framework for the simulation of complex physical systems. The framework leverages the extreme…
Soft materials such as rubbers, hydrogels, and biological tissues undergo damage in the form of stiffness degradation without apparent changes in their stress-free geometry. Accurate simulation of this behavior is critical in applications…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
This paper presents a new finite difference method, called {\varphi}-FD, inspired by the {\phi}-FEM approach for solving elliptic partial differential equations (PDEs) on general geometries. The proposed method uses Cartesian grids,…
The true power of computational research typically can lay in either what it accomplishes or what it enables others to accomplish. In this work, both avenues are simultaneously embraced across several distinct efforts existing at three…
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…
To solve large-scale or high-resolution topology optimization problem, a novel algorithm is developed based on modified bi-directional evolutionary structure optimization (BESO) and extended finite element method (XFEM). Within XFEM, a set…
Power efficiency is plateauing in the standard digital electronics realm such that novel hardware, models, and algorithms are needed to reduce the costs of AI training. The combination of energy-based analog circuits and the Equilibrium…
This paper presents PowerModelsADA, an open-source framework for solving Optimal Power Flow (OPF) problems using Alternating Distributed Algorithms (ADA). PowerModelsADA provides a framework to test, verify, and benchmark both existing and…
Adaptive gradient methods have shown excellent performances for solving many machine learning problems. Although multiple adaptive gradient methods were recently studied, they mainly focus on either empirical or theoretical aspects and also…
The solution of physical problems discretized using the finite element methods using quantum computers remains relatively unexplored. Here, we present a unified formulation (FEqa) to solve such problems using quantum annealers. FEqa is a…
This work develops novel energy-stable parametric finite element methods (ES-PFEM) for the Willmore flow and curvature-dependent geometric gradient flows of surfaces in three dimensions. The key to achieving the energy stability lies in the…
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns…
Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering…
A new method for implementing the kinetic energy operator for real-space, grid-based electronic structure codes is developed. It is based on multi-order Adaptive Finite Differencing (AFD) and uses atomic pseudo orbitals produced by the…
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
In this paper, we explore the use of the Virtual Element Method concepts to solve scalar and system hyperbolic problems on general polygonal grids. The new schemes stem from the active flux approach \cite{AF1}, which combines the usage of…
Computational Fluid Dynamics (CFD) simulations are essential for analyzing and optimizing fluid flows in a wide range of real-world applications. These simulations involve approximating the solutions of the Navier-Stokes differential…
Finite element (FE) analysis guides the design and verification of nearly all manufactured objects. It is at the core of computational engineering, enabling simulation of complex physical systems, from fluids and solids to multiphysics…
In recent years, high performance scientific computing on graphics processing units (GPUs) have gained widespread acceptance. These devices are designed to offer massively parallel threads for running code with general purpose. There are…