相关论文: A fast direct solver for two dimensional quasi-per…
Most discussions of chaotic scattering systems are devoted to two-dimensional systems. It is of considerable interest to extend these studies to the, in general, more realistic case of three dimensions. In this context, it is conceptually…
We propose a direct imaging method based on the reverse time migration to reconstruct extended obstacles in the half space with finite aperture elastic scattering data at a fixed frequency. We prove the resolution of the reconstruction…
We present a fast iterative solver for scattering problems in 2D, where a penetrable object with compact support is considered. By representing the scattered field as a volume potential in terms of the Green's function, we arrive at the…
We present a sharp collocated projection method for solving the immiscible, two-phase Navier-Stokes equations in two- and three-dimensions. Our method is built using non-graded adaptive quadtree and octree grids, where all of the fluid…
We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…
Scattering at interluminal modulation interfaces, where a sharp space-time perturbation moves at a velocity lying between the wave velocities of the two surrounding media, has remained an open problem for decades. This regime is somewhat…
In this article we consider two-grid finite element methods for solving semilinear interface problems in d space dimensions, for d=2 or d=3. We first describe in some detail the target problem class with discontinuous diffusion…
In this paper, given a linear system of equations A x = b, we are finding locations in the plane to place objects such that sending waves from the source points and gathering them at the receiving points solves that linear system of…
Large-scale metasurfaces promise nanophotonic performance improvements to macroscopic optics functionality, for applications from imaging to analog computing. Yet the size scale mismatch of centimeter-scale chips versus micron-scale…
Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…
We consider scalar decentralized average-cost infinite-horizon LQG problems with two controllers, focusing on the fast dynamics case when the (scalar) eigenvalue of the system is large. It is shown that the best linear controllers'…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…
Wave propagation in multilayered media with high material contrasts poses significant numerical challenges, as large variations in wavenumbers lead to strong reflections and complex transmission of the incoming wave field. To address these…
A method is developed for solving quasilinear convection diffusion problems starting on a coarse mesh where the data and solution-dependent coefficients are unresolved, the problem is unstable and approximation properties do not hold. The…
We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
Achieving exact unidirectional invisibility in a finite frequency band has been an outstanding problem for many years. We offer a simple solution to this problem in two dimensions that is based on our solution to another more basic open…
In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…