Related papers: On optimality and bounds for internal solutions ge…
We treat the calculation of gravitational radiation using the mixed timelike-null initial value formulation of general relativity. The determination of an exterior radiative solution is based on boundary values on a timelike worldtube…
We prove decay estimates in the interior for solutions to elliptic equations in divergence form with Lipschitz continuous coefficients. The estimates explicitly depend on the distance from the boundary and on suitable notions of frequency…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the $L^2$-Tikhonov regularization method, we analyze its convergence under two…
Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a…
In this paper we approximate the convex envelope of a boundary datum inside a bounded domain in the Euclidean space. We work with a random graph that is obtained as random points with uniform distribution that are connected by proximity…
In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic geometry of the domain across which observations are…
We investigate the inverse Cauchy and data completion problems for elliptic partial differential equations in a bounded domain $D \subset \mathbb{R}^d$, $d \ge 2$, with a special emphasis on the steady-state heat conduction in anisotropic…
Boundary detection has long been a fundamental tool for image processing and computer vision, supporting the analysis of static and time-varying data. In this work, we built upon the theory of Graph Signal Processing to propose a novel…
Quadrature-based approximation of Gramians in standard balanced truncation yields a non-intrusive, data-driven implementation that requires only transfer function samples on the imaginary axis, which can be measured experimentally. This…
We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider…
In two phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry…
GS2 is an initial value gyrokinetic simulation code developed to study low-frequency turbulence in magnetized plasma. It is parallelised using MPI with the simulation domain decomposed across tasks. The optimal domain decomposition is…
In the present work the linearized problem of plasma wave reflection from a boundary of a half--space is solved analytically. Specular accommodative conditions of plasma wave reflection from plasma boundary are taken into consideration.…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
Diffuse domain methods (DDMs) have gained significant attention for solving partial differential equations (PDEs) on complex geometries. These methods approximate the domain by replacing sharp boundaries with a diffuse layer of thickness…
Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows…
We show that sparsity constrained optimization problems over low dimensional spaces tend to have a small duality gap. We use the Shapley-Folkman theorem to derive both data-driven bounds on the duality gap, and an efficient primalization…
Perfectly Matched Layers (PML) has become a very common method for the numerical approximation of wave and wave-like equations on unbounded domains. This technique allows one to obtain accurate solutions while working on a finite…
Gaussian processes (GPs) are widely used as surrogate models for emulating computer code, which simulate complex physical phenomena. In many problems, additional boundary information (i.e., the behavior of the phenomena along input…