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Topology optimization is a key methodology in engineering design for finding efficient and robust structures. Due to the enormous size of the design space, evaluating all possible configurations is typically infeasible. In this work, we…
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…
This paper proposes a methodology to estimate stress in the subsurface by a hybrid method combining finite element modeling and neural networks. This methodology exploits the idea of obtaining a multi-frequency solution in the numerical…
We present a variational quantum algorithm for structural mechanical problems, specifically addressing crack opening simulations that traditionally require extensive computational resources. Our approach provides an alternative solution for…
Molecular dynamics simulations are a central computational methodology in materials design for relating atomic composition to mechanical properties. However, simulating materials with atomic-level resolution on a macroscopic scale is…
FLAME is a software package to perform a wide range of atomistic simulations for exploring the potential energy surfaces (PES) of complex condensed matter systems. The range of methods include molecular dynamics simulations to sample free…
Particle filtering is a numerical Bayesian technique that has great potential for solving sequential estimation problems involving non-linear and non-Gaussian models. Since the estimation accuracy achieved by particle filters improves as…
This work presents a practical finite element modeling strategy, the Crack Element Method (CEM), for simulating the dynamic crack propagation in two-dimensional structures. The method employs an element-splitting algorithm based on the…
The Finite element method (FEM) has long served as the computational backbone for topology optimization (TO). However, for designing structures undergoing large deformations, conventional FEM-based TO often exhibits numerical instabilities…
This paper presents a computational model, based on the Finite Element Method (FEM), that simulates the thermal response of laser-irradiated tissue. This model addresses a gap in the current ecosystem of surgical robot simulators, which…
Modern computing systems are capable of exascale calculations, which are revolutionizing the development and application of high-fidelity numerical models in computational science and engineering. While these systems continue to grow in…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
Aircraft design optimization traditionally relies on computationally expensive simulation techniques such as Finite Element Method (FEM) and Finite Volume Method (FVM), which, while accurate, can significantly slow down the design iteration…
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…
Several authors have employed Finite Element Analysis (FEA) for stress and strain analysis in orthopaedic biomechanics. Unfortunately, the use of three-dimensional models is time consuming and consequently the number of analysis to be…
Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…
In this work, we present a parallel, fully-distributed finite element numerical framework to simulate the low-frequency electromagnetic response of superconducting devices, which allows to efficiently exploit HPC platforms. We select the…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…