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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The core-shell obstacle scattering in a multilayered medium
多层介质 核壳障碍物 散射 边界积分方程
2023/4/26
Scattering from the coated targets embedded in a multilayered medium has attracted much interest during recent years for extensive applications, such as sea radar target detection and underwater radar...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：ENERGY, POINTWISE, AND FREE BOUNDARY APPROXIMATION OF THE OBSTACLE PROBLEM FOR NONLOCAL OPERATORS
非局部 算子障碍物 自由边界 近似
2023/4/28
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order $s \in (0,1)$. We derive regularity results in weighted Sobolev spaces, where the wei...
Random Homogenization of Fractional Obstacle Problems
Random Homogenization Fractional Obstacle Problems
2015/10/15
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
We study the homogenization of an obstacle problem in a perforated domain, when the holes are periodically distributed and have random shape and size. The main assumption concerns the capacity of the ...
Obstacle collision detection using best ellipsoid fit
ellipsoid fit geometric approximation collision detection
2015/8/11
This paper describes a method for estimating the distance between a robot and its surrounding environment using best ellipsoid fit. The method consists of the following two stages. First we approximat...
DIRECTIONAL PRECONDITIONER FOR HIGH FREQUENCY OBSTACLE SCATTERING
Boundary integral method scattering high-frequency waves preconditioner low-rank approximation sparse linear algebra
2015/7/14
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterativ...
A Cubic Spline Method for Solving a Unilateral Obstacle Problem
Obstacle Problem Spline Collocation Nonsmooth Equation Generalized Newton Method
2013/1/30
This paper, we develop a numerical method for solving a unilateral obstacle problem by using the cubic spline collocation method and the generalized Newton method. This method converges quadratically ...
Stochastic differential games involving impulse controls and double-obstacle quasi-variational inequalities
Stochastic differential game Impulse control Quasi-variational inequality Viscosity solution
2012/6/25
We study a two-player zero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equati...
C^{1,1} regularity for degenerate elliptic obstacle problems in mathematical finance
American-style option degenerate elliptic differential operator degenerate diffusion process free boundary problem Heston stochastic volatility process
2012/6/21
The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the h...
Growth rates, Hausdorff measure and stability for the p-obstacle problem(3/2≤p≤2)
growth rate Hausdorff measure obstacle problem stability
2011/10/17
In this paper, we consider the free boundary for the inho-mogeneous obstacle problem with zero obstacle. We firstly establish the growth rates for the solution u(x) and the gradient of u(x), awa...
Computing the obstacle number of a plane graph
obstacle number of a plane graph Computational Geometry
2011/10/9
Abstract: An obstacle representation of a plane graph G is V(G) together with a set of opaque polygonal obstacles such that G is the visibility graph on V(G) determined by the obstacles. We investigat...
The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval II. Obstacles with a dissipative boundary or finite refractive index and back-scattering data
enclosure method inverse obstacle scattering problem inverse backscattering obstacle wave equation dissipative boundary condition
2011/9/5
Abstract: In this paper a wave is generated by an initial data whose support is localized at the outside of unknown obstacles and observed in a limited time on a known closed surface or the same posit...
Numerical Solution of Obstacle Problems by B-Spline Functions
Least Square Method Uniform B-Splines Boundary Value Problems Obstacle Problems
2013/1/30
In this study, we use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems. The pro...
Small (2,s)-colorable graphs without 1-obstacle representations
Small (2,s)-colorable graphs 1-obstacle representations
2011/3/4
An obstacle representation of a graph G is a set of points on the plane together with a set of polygonal obstacles that determine a visibility graph isomorphic to G. The obstacle number of G is the mi...
Stability of the solution to inverse obstacle scattering problem
inverse obstacle scattering problem math
2010/11/1
It is proved that if the scattering amplitudes at a fixed wavenumber for two obstacles from a certain large class of obstacles differ a little, than the obstacles differ a little. Error estimate is g...