Related papers: The Matrix Element Method: Past, Present, and Futu…
This work illustrates the possibility to apply the Fast Fourier Transformation to obtain the integrals of the Boundary Element Method (BEM) on arbitrary shapes. The procedure is inspired by the technique used with great success within the…
The Boundary Element Method (BEM) is implemented using piecewise linear elements to solve the two-dimensional Dirichlet problem for Laplace's equation posed on a disk. A benefit of the BEM as opposed to many other numerical solution…
In the past fifteen years mathematical models for microelectromechanical systems (MEMS) have been the subject of several studies, in particular due to the interesting qualitative properties they feature. Still most research is devoted to an…
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…
This paper provides a mixture modeling framework using the bivariate generalized exponential distribution. We study different properties of this mixture distribution. Hierarchical EM algorithm is developed for finding the estimates of the…
We formulate a new atomistic/continuum (a/c) coupling scheme that employs the boundary element method (BEM) to obtain an improved far-field boundary condition. We establish sharp error bounds in a 2D model problem for a point defect…
This study presents a generalized multiscale multimesh finite element method ($\text{M}^2$-FEM) that addresses several long-standing challenges in the numerical simulation of integral structural theories, often used to model multiscale and…
A framework is introduced for expressing electromagnetic (EM) potentials and fields of single atomic or molecular emitters modeled as oscillating dipoles, which follows a recently proposed method for solving inhomogeneous wave equations for…
Multi-energy computed tomography (ME-CT) is an x-ray transmission imaging technique that uses the energy dependence of x-ray photon attenuation to determine the elemental composition of an object of interest. Mathematically, forward ME-CT…
The present work deals with the formulation of a Virtual Element Method (VEM) for two dimensional structural problems. The contribution is split in two parts: in part I, the elastic problem is discussed, while in part II [3] the method is…
The virtual element method (VEM) allows discretization of the problem domain with polygons in 2D. The polygons can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing…
The promise of machine learning has been explored in a variety of scientific disciplines in the last few years, however, its application on first-principles based computationally expensive tools is still in nascent stage. Even with the…
Here, we present an overview of recent developments in the characterization of electromagnetic and quantum metamaterials using effective medium methods. It is highlighted that both electromagnetic and electronic systems can be homogenized…
Simulation of fracturing processes in porous rocks can be divided into two main branches: (i) modeling the rock as a continuum which is enhanced with special features to account for fractures, or (ii) modeling the rock by a discrete (or…
This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…
The class of memory circuit elements which comprises memristive, memcapacitive, and meminductive systems, is gaining considerable attention in a broad range of disciplines. This is due to the enormous flexibility these elements provide in…
To accelerate learning process with few samples, meta-learning resorts to prior knowledge from previous tasks. However, the inconsistent task distribution and heterogeneity is hard to be handled through a global sharing model…
Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle…
This note describes an extended exercise on the finite-element (FE) simulation of an accelerator magnet. The students construct and simulate a magnet model using the FEMM freeware. They get the opportunity to exercise on the theory of FEs,…
In the study of complex systems, evaluating physical observables often requires sampling representative configurations via Monte Carlo techniques. These methods rely on repeated evaluations of the system's energy and force fields, which can…