Related papers: Spectral/hp element methods: recent developments, …
This paper presents a new data-driven finite element framework that is applicable to a broad range of engineering simulation problems. In the data-driven approach, the conservation laws and boundary conditions are satisfied by means of the…
In this paper, we propose an approach for solving PDEs on evolving surfaces using a combination of the trace finite element method and a fast marching method. The numerical approach is based on the Eulerian description of the surface…
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 introduce adaptive particle refinement for compressible smoothed particle hydrodynamics (SPH). SPH calculations have the natural advantage that resolution follows mass, but this is not always optimal. Our implementation allows the user…
We develop an enrichment wall-model within the spectral element method (SEM) framework for large-eddy simulations of wall-bounded flows. The method augments the polynomial solution in the wall-adjacent elements with an analytical…
Smoothed Particle Hydrodynamics (SPH) methods are advantageous in simulations of fluids in domains with free boundary. Special SPH methods have also been developed to simulate solids. However, there are situations where the matter behaves…
We have been constructed a brand-new radiation hydrodynamics solver based upon Smoothed Particle Hydrodynamics (SPH), which works on parallel computer system. The code is designed to investigate the formation and evolution of the first…
Smoothed Particle Hydrodynamics (SPH_ is a mesh-free Lagrangian method renowned for modeling large deformations and free-surface flows, yet classical formulations remain confined to deterministic systems. We introduce Stochastic SPH…
An $hp$-adaptive continuous Galerkin finite element method is developed to analyze a static anti-plane shear crack embedded in a nonlinear, strain-limiting elastic body. The geometrically linear material is described by a constitutive law…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
Group synchronization asks to recover group elements from their pairwise measurements. It has found numerous applications across various scientific disciplines. In this work, we focus on orthogonal and permutation group synchronization…
We consider in this paper the Hahn polynomials and their application in numerical methods. The Hahn polynomials are classical discrete orthogonal polynomials. We analyse the behaviour of these polynomials in the context of spectral…
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…
The pseudospectral method is a powerful tool for finding highly precise solutions of Schr\"{o}dinger's equation for few-electron problems. We extend the method's scope to wave functions with non-zero angular momentum and test it on several…
Starting with some fundamental concepts, in this article we present the essential aspects of spectral methods and their applications to the numerical solution of Partial Differential Equations (PDEs). We start by using Lagrange and…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…
This paper presents a novel stabilized nonconforming finite element method for solving the surface biharmonic problem. The method extends the New-Zienkiewicz-type (NZT) element to polyhedral (approximated) surfaces by employing the Piola…
We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial vector field and finding integrals of polynomial…