Related papers: On Domain Decomposition for Magnetostatic Problems…
Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…
This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…
Simultaneous matrix diagonalization is used as a subroutine in many machine learning problems, including blind source separation and paramater estimation in latent variable models. Here, we extend algorithms for performing joint…
In this series of papers we examine magnetic reconnection in a domain where the magnetic field does not vanish and the non-ideal region is localised in space. In a previous paper we presented a technique for obtaining analytical solutions…
Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global…
Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage.…
We propose a simple domain decomposition method for $d$-dimensional elliptic PDEs which involves an overlapping decomposition into local subdomain problems and a global coarse problem. It relies on a space-filling curve to create equally…
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…
Isogeometric analysis (IGA) is used to simulate a permanent magnet synchronous machine. IGA uses non-uniform rational B-splines to parametrise the domain and to approximate the solution space, thus allowing for the exact description of the…
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…
Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum…
In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface…
This work deals with shape optimization of electric machines using isogeometric analysis. Isogeometric analysis is particularly well suited for shape optimization as it allows to easily modify the geometry without remeshing the domain. A…
Semantic segmentation models only perform well on the domain they are trained on and datasets for training are scarce and often have a small label-spaces, because the pixel level annotations required are expensive to make. Thus training…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
In this article, a few problems related to multiscale modelling of magnetic materials at finite temperatures and possible ways of solving these problems are discussed. The discussion is mainly centred around two established multiscale…
This paper gives a geometric description of functional spaces related to Domain Decomposition techniques for computing solutions of Laplace and Helmholtz equations. Understanding the geometric structure of these spaces leads to algorithms…
The patch dynamics scheme in equation-free multiscale modelling can efficiently predict the macroscopic behaviours by simulating the microscale problem in a fraction of the space-time domain. The patch dynamics schemes developed so far, are…
A key scalability challenge in neural solvers for industrial-scale physics simulations is efficiently capturing both fine-grained local interactions and long-range global dependencies across millions of spatial elements. We introduce the…
Multi contrast MRI synthesis is inherently challenging due to the complex and nonlinear relationships among different contrasts. Each MRI contrast highlights unique tissue properties, but their complementary information is difficult to…