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We introduce an enriched immersed finite element method for addressing interface problems characterized by general non-homogeneous jump conditions. Unlike many existing unfitted mesh methods, our approach incorporates a homogenization…
We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…
Modeling dynamics in the form of partial differential equations (PDEs) is an effectual way to understand real-world physics processes. For complex physics systems, analytical solutions are not available and numerical solutions are…
Inverse problems for Partial Differential Equations (PDEs) are crucial in numerous applications such as geophysics, biomedical imaging, and material science, where unknown physical properties must be inferred from indirect measurements. In…
We construct and analyze a group of immersed finite element (IFE) spaces formed by linear, bilinear and rotated Q1 polynomials for solving planar elasticity equation involving interface. The shape functions in these IFE spaces are…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
The parallel full approximation scheme in space and time (PFASST) is a parallel-in-time integrator that allows to integrate multiple time-steps simultaneously. It has been shown to extend scaling limits of spatial parallelization strategies…
Test optimization contains test case selection and minimization, which is an important challenge in software testing and has been addressed with search-based approaches intensively in the past. Inspired by the recent advancement of using…
At its critical point, the three-dimensional lattice Ising model is described by a conformal field theory (CFT), the 3d Ising CFT. Instead of carrying out simulations on Euclidean lattices, we use the Quantum Finite Elements method to…
A new LISA simulator (LISACode) is presented. Its ambition is to achieve a new degree of sophistication allowing to map, as closely as possible, the impact of the different sub-systems on the measurements. LISACode is not a detailed…
The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an…
Microwave Imaging is an essential technique for reconstructing the electrical properties of an inaccessible medium. Many approaches have been proposed employing algorithms to solve the Electromagnetic Inverse Scattering Problem associated…
Dynamic programming (DP) is a fundamental and powerful algorithmic paradigm taught in most undergraduate (and many graduate) algorithms classes. DP problems are challenging for many computer science students because they require identifying…
The infinite time-evolving block decimation (iTEBD) algorithm [Phys. Rev. Lett. 98, 070201 (2007)] allows to simulate unitary evolution and to compute the ground state of one-dimensional quantum lattice systems in the thermodynamic limit.…
This paper presents a 55-line code written in python for 2D and 3D topology optimization (TO) based on the open-source finite element computing software (FEniCS), equipped with various finite element tools and solvers. PETSc is used as the…
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…
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…
Differentiable programming opens exciting new avenues in particle physics, also affecting future event generators. These new techniques boost the performance of current and planned MadGraph implementations. Combining phase-space mappings…
We discuss how to implement the linear finite element method for solving the Poisson equation. We begin with the data structure to represent the triangulation and boundary conditions, introduce the sparse matrix, and then discuss the…
Quantum impurity solvers have a broad range of applications in theoretical studies of strongly correlated electron systems. Especially, they play a key role in dynamical mean-field theory calculations of correlated lattice models and…