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We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…
We introduce \texttt{featom}, an open source code that implements a high-order finite element solver for the radial Schr\"odinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or…
Recent developments in x-ray science provide methods to probe deeply embedded mesoscale grain structures and spatially resolve them using dark field x-ray microscopy (DFXM). Extending this technique to investigate weak diffraction signals…
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…
An efficient and easy-to-implement method is proposed to regularize integral equations in the 3D boundary element method (BEM). The method takes advantage of an assumed three-noded triangle discretization of the boundary surfaces. The…
The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…
An accurate, physically-based, and differentiable model of soft robots can unlock downstream applications in optimal control. The Finite Element Method (FEM) is an expressive approach for modeling highly deformable structures such as…
This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…
The extended finite element method (XFEM) was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to be split by a discontinuity, strong…
A finite element method (FEM) for solving the complex valued k({\omega}) vs. {\omega} dispersion curve of a 3D metamaterial/photonic crystal system is presented. This 3D method is a generalization of a previously reported 2D eigenvalue…
Hybrid algorithms, which combine black-box machine learning methods with experience from traditional numerical methods and domain expertise from diverse application areas, are progressively gaining importance in scientific machine learning…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
Digital MemComputing machines (DMMs), which employ nonlinear dynamical systems with memory (time non-locality), have proven to be a robust and scalable unconventional computing approach for solving a wide variety of combinatorial…
A general method to generate a centrosymmetric matrix associated with the solving of partial differential equation (PDE) on an irreducible domain by means of a linear equation system is proposed. The method applies to any PDE for which both…
Precise tracking and measurement of the energy carried by the individual magnetohydrodynamic (MHD) modes has important implications and utility in astrophysical and laboratory plasmas. Previously, this was only achievable in limited linear…
Density matrix embedding theory (DMET) is a powerful quantum embedding method for solving strongly correlated quantum systems. Theoretically, the performance of a quantum embedding method should be limited by the computational cost of the…
In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
Finite-element (FE) discretisations have emerged as a powerful real-space alternative to large-scale Kohn-Sham density functional theory (DFT) calculations, offering systematic convergence, excellent parallel scalability, while…
The potential of neural networks (NN) in engineering is rooted in their capacity to understand intricate patterns and complex systems, leveraging their universal nonlinear approximation capabilities and high expressivity. Meanwhile,…