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We propose an algorithm for the efficient parallel implementation of elastoplastic problems with hardening based on the so-called TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. We consider an…
Electrical machines employing superconductors are attractive solutions in a variety of application domains. Numerical models are powerful and necessary tools to optimize their design and predict their performance. The electromagnetic…
The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for "intermediate" potentials…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…
It is shown that the behavior of an $m$-port circuit of maximal monotone elements can be expressed as a zero of the sum of a maximal monotone operator containing the circuit elements, and a structured skew-symmetric linear operator…
Time-periodic form or expression is a ubiquitous natural and man-made phenomenon observable in all the scientific and engineering disciplines. In this article, we propose a theory of periodic sequence (TPS), which can be formulated as a…
This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of…
We analyse a numerical method for the coupled system of the eddy current equations in $\mathbb{R}^3$ with the Landau-Lifshitz-Gilbert equation in a bounded domain. The unbounded domain is discretised by means of…
Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is…
In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear,…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
Parallel simulation and control of large-scale robotic systems often rely on partitioned time stepping, yet finite-iteration coupling can inject spurious energy by violating power consistency--even when each subsystem is passive. This…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
We propose a new discretization method for PDEs on moving domains in the setting of unfitted finite element methods, which is provably higher-order accurate in space and time. In the considered setting, the physical domain that evolves…
We perform model-independent analyses extracting limits for the electric dipole moment of the electron and the P,T-odd scalar-pseudoscalar (S-PS) nucleon-electron coupling from the most recent measurements with atoms and molecules. The…
Time-encoding of continuous-time signals is an alternative sampling paradigm to conventional methods such as Shannon's sampling. In time-encoding, the signal is encoded using a sequence of time instants where an event occurs, and hence fall…
The accurate electromagnetic modeling of both low- and high-frequency physics is crucial in the signal and power integrity analysis of electrical interconnects. The boundary element method (BEM) is appealing for lossy conductor modeling…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…
Structured Finite Element Methods (FEMs) based on low-rank approximation in the form of the so-called Quantized Tensor Train (QTT) decomposition (QTT-FEM) have been proposed and extensively studied in the case of elliptic equations. In this…