Related papers: An adaptive finite element/finite difference domai…
In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the…
With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; \Omega)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high…
We employ ptychography, a phase-retrieval imaging technique, to show experimentally for the first time that a partially coherent high-energy matter (electron) wave emanating from an extended source can be decomposed into a set of mutually…
A new set of vector solutions to Maxwell's equations based on solutions to the wave equation in spheroidal coordinates allows laser beams to be described beyond the paraxial approximation. Using these solutions allows us to calculate the…
We consider the problem of solving partial differential equations (PDEs) in domains with complex microparticle geometry that is impractical, or intractable, to model explicitly. Drawing inspiration from volume rendering, we propose tackling…
This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…
The simulation of three dimensional magnetostatic problems plays an important role, for example when simulating synchronous electric machines. Building on prior work that developed a domain decomposition algorithm using isogeometric…
We consider the numerical reconstruction of the spatially dependent conductivity coefficient and the source term in elliptic partial differential equations in a two-dimensional convex polygonal domain, with the homogeneous Dirichlet…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\infty$ coefficients. The methods are of Galerkin type and follow the…
We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the…
We demonstrate the application of the Dynamic Mode Decomposition (DMD) for the diagnostic analysis of the nonlinear dynamics of a magnetized plasma in resistive magnetohydrodynamics. The DMD method is an ideal spatio-temporal matrix…
A space-time domain decomposition approach is presented as a natural extension of the enhanced velocity mixed finite element (EVMFE) [Wheeler et. al] for spatial domain decomposition. The proposed approach allows for different space-time…
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space…
In this work we design a new domain decomposition method for the Euler equations in 2 dimensions. The basis is the equivalence via the Smith factorization with a third order scalar equation to whom we can apply an algorithm inspired from…
Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori…
End-to-end deep learning improves breast cancer classification on diffusion-weighted MR images (DWI) using a convolutional neural network (CNN) architecture. A limitation of CNN as opposed to previous model-based approaches is the…
This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…
We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field during materials processing. Our numerical approach uses the systematic renormalization-group formulation of the phase field…