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We simulate the electrical response of multiple disjoint biological 3D cells undergoing an electropermeabilization process. Instead of solving the boundary value problem in the unbounded volume, we reduce it to a system of boundary…
In certain practical engineering applications, there is an urgent need to perform repetitive solving of partial differential equations (PDEs) in a short period. This paper primarily considers three scenarios requiring extensive repetitive…
The Darwin field model addresses an approximation to Maxwell's equations where radiation effects are neglected. It allows to describe general quasistatic electromagnetic field phenomena including inductive, resistive and capacitive effects.…
Drift-diffusion plasma fluid models are commonly used to simulate electric discharges. Such models can computationally be very efficient if they are combined with explicit time integration. This paper deals with two issues that often arise…
One promising decomposition of turbulent dynamics is that into building blocks such as equilibrium and periodic solutions and orbits connecting these. While the numerical approximation of such building blocks is feasible for flows in small…
We introduce a generalization of time-domain wavefield reconstruction inversion to anisotropic acoustic modeling. Wavefield reconstruction inversion has been extensively researched in recent years for its ability to mitigate cycle skipping.…
We investigate the behavior of the time derivatives of the solution to a linear time-fractional, advection-diffusion-reaction equation, allowing space- and time-dependent coefficients as well as initial data that may have low regularity.…
We embed general boundary value problems for the time-harmonic Maxwell equations into the elliptic boundary value theory. This is achieved by introducing two new scalar functions to the electromagnetic field and imposing additional boundary…
Harmonic and transient eddy currents in a liquid metal positioned above an excitation coil are determined by measuring the voltage drop in a simple potential probe. The resulting spatio-temporal eddy current field is compared with the…
We consider waveform iterations for dynamical coupled problems, or more specifically, PDEs that interact through a lower dimensional interface. We want to allow for the reuse of existing codes for the subproblems, called a partitioned…
Isogeometric Analysis is a variant of the finite element method, where spline functions are used for the representation of both the geometry and the solution. Splines, particularly those with higher degree, achieve their full approximation…
We consider for the time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic measurements of the…
The interior resonance problem of time domain integral equations (TDIEs) formulated to analyze acoustic field interactions on penetrable objects is investigated. Two types of TDIEs are considered: The first equation, which is termed the…
Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…
Frequency domain Mie solutions to scattering from spheres have been used for a long time. However, deriving their transient analogue is a challenge as it involves an inverse Fourier transform of the spherical Hankel functions (and their…
This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power…
The FETI-DP algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp.~1235--1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp.~128--149] for solving incompressible Stokes equations, are extended to…
In this work, we develop a space--time Chebyshev spectral collocation method for three-dimensional Maxwell's equations and combine it with tensor-network techniques in Tensor-Train (TT) format. Under constant material parameters, the…
A time-domain approach is proposed for the propagation of ultrashort electro- magnetic wave packets beyond the paraxial and the slowly-varying-envelope approximations. An analytical method based on perturbation theory is used to solve the…
We describe a simple and intuitive implementation of the method of finite difference time domain simulations for propagating electromagnetic waves using the simplest possible tools available in Microsoft Excel. The method overcomes the…