Related papers: Comparative study of different quadrature methods …
This work presents an efficient quadrature rule for shell analysis fully integrated in CAD by means of Isogeometric Analysis (IGA). General CAD-models may consist of trimmed parts such as holes, intersections, cut-offs etc. Therefore, IGA…
We introduce and analyze a robust nonconforming finite element method for a three dimensional singularly perturbed quad-curl model problem. For the solution of the model problem, we derive proper a priori bounds, based on which, we prove…
In computational biology and other sciences, researchers are frequently faced with a choice between several computational methods for performing data analyses. Benchmarking studies aim to rigorously compare the performance of different…
We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the…
Fourth order curvature driven interface evolution equations frequently appear in the natural sciences. Often axisymmetric geometries are of interest, and in this situation numerical computations are much more efficient. We will introduce…
Near-term hardware is constrained by high error rates, small qubit counts, and relatively low output fidelity, making the execution of large, high performance quantum circuits difficult. Circuit partitioning (or circuit cutting) has emerged…
Nowadays, high-speed machining is usually used for production of hardened material parts with complex shapes such as dies and molds. In such parts, tool paths generated for bottom machining feature with the conventional parallel plane…
In the current practices of both industry and academia, the convergence and accuracy of finite element calculations are closely related to the methods and quality of mesh generation. For years, the research on high-quality mesh generation…
This paper presents a technique for stress and fracture analysis by using the scaled boundary finite element method (SBFEM) with quadtree mesh of high-order elements. The cells of the quadtree mesh are modelled as scaled boundary polygons…
This research paper aims to find, analyze and understand code patterns in any software system and measure its quality by defining standards and proposing a formula for the same. Every code that is written can be divided into different code…
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…
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…
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 finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…
We describe a three-stage procedure to analyze the dependence of Poisson Boltzmann calculations on the shape, size and geometry of the boundary between solute and solvent. Our study is carried out within the boundary element formalism, but…
Open source software is becoming crucial in the design and testing of quantum algorithms. Many of the tools are backed by major commercial vendors with the goal to make it easier to develop quantum software: this mirrors how well-funded…
In recent years, a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on non-matching or overlapping meshes. Examples of such methods include the fictitious…
Finite elements of higher continuity, say conforming in $H^2$ instead of $H^1$, require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to…
The design, implementation and analysis of a free library for boundary element calculations is presented. The library is free in the sense of the GNU General Public Licence and is intended to allow users to solve a wide range of problems…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…