Papers by Sebastian Acosta
High Order Local Farfield Expansions Absorbing Boundary Conditions for Multiple Scattering
SSRN Electronic Journal, 2021
Wave Motion, 2020
Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally ... more Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high order local absorbing boundary conditions (ABCs) with finite difference methods for the Helmholtz equation. These ABCs are based on exact representations of the outgoing waves by means of farfield expansions. The finite difference methods, which are constructed from a deferred-correction (DC) technique, approximate the Helmholtz equation and the ABCs, with the appropriate number of terms, to any desired order. As a result, high order numerical methods with an overall order of convergence equal to the order of the DC schemes are obtained. A detailed construction of these DC finite difference schemes is presented. Additionally, a rigorous proof of the consistency of the DC schemes with the Helmholtz equation and the ABCs in polar coordinates is also given. The results of several numerical experiments corroborate the high order convergence of the novel method.
Electronic transactions on numerical analysis ETNA
Two new quasi-linear elliptic systems of partial differential equations to automatically generate... more Two new quasi-linear elliptic systems of partial differential equations to automatically generate two-dimensional boundary conforming structured grids are formulated. One of the new systems generates grids with near-uniform cell areas. The other produces meshes with near-uniform coordinate line spacings. In both cases, the resulting grids conform to complex boundaries with severe singularities without self-overlapping. In contrast with other elliptic generators, the control functions are held as dependent variables. They obey Poisson-type equations with appropriate forcing. Grid quality analysis reveals the advantage in terms of smoothness and cell area uniformity of the new grids compared with other structured grids. An efficient procedure to combine the novel elliptic grids with algebraic grids for large domains is devised.
Inverse Problems and Imaging, 2015
In this paper, we investigate the recovery of the absorption coefficient from boundary data assum... more In this paper, we investigate the recovery of the absorption coefficient from boundary data assuming that the region of interest is illuminated at an initial time. We consider a sufficiently strong and isotropic, but otherwise unknown initial state of radiation. This work is part of an effort to reconstruct optical properties using unknown illumination embedded in the unknown medium. We break the problem into two steps. First, in a linear framework, we seek the simultaneous recovery of a forcing term of the form σ(t, x, θ)f (x) (with σ known) and an isotropic initial condition u 0 (x) using the single measurement induced by these data. Based on exact boundary controllability, we derive a system of equations for the unknown terms f and u 0 . The system is shown to be Fredholm if σ satisfies a certain positivity condition. We show that for generic term σ and weakly absorbing media, this linear inverse problem is uniquely solvable with a stability estimate. In the second step, we use the stability results from the linear problem to address the nonlinearity in the recovery of a weak absorbing coefficient. We obtain a locally Lipschitz stability estimate.
Inverse Problems & Imaging, 2015
In this paper we consider the problem of recovering the conformal factor in a conformal class of ... more In this paper we consider the problem of recovering the conformal factor in a conformal class of Riemannian metrics from the boundary measurement of one wave field. More precisely, using boundary control operators, we derive an explicit equation satisfied by the contrast between two conformal factors (or wave speeds). This equation is Fredholm and generically invertible provided that the domain of interest is properly illuminated at an initial time. We also show locally Lipschitz stability estimates.
Elliptic grid generation methods for scattering from multiple obstacles
PAMM, 2007
A novel finite difference time domain method for acoustic scattering on generalized curvilinear c... more A novel finite difference time domain method for acoustic scattering on generalized curvilinear coordinates is briefly described. Scattering over two‐dimensional complex regions consisting of multiple scatterers are analyzed. The grid generation algorithm decomposes regions with finite number of holes to contiguous single‐hole subregions. Individual grids are obtained for each subregions and they are matched with smoothness across interfaces. The new algorithm is an extension to multiple obstacles of the technique introduced in [V. Villamizar, M. Weber, Boundary‐Conforming Cordinates with Grid Line Control for Acoustic Scattering from Complexly Shaped Obstacles, Numer. Meth. Part Differ. Equ. 23 (2007) 1445–1467]. The method is successfully applied to approximate the pressure field resulting from the acoustic scattering of a plane wave from two complexly‐shaped obstacles. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mathematics and Computers in Simulation, 2009
A new approach to generate structured grids for two-dimensional multiply connected regions with s... more A new approach to generate structured grids for two-dimensional multiply connected regions with several holes is proposed. The bounding curves may include corners or cusps. The new algorithm constitutes an extension of the Branch Cut Grid Line Control (BCGC) technique introduced byVillamizar et al. [V. Villamizar, O. Rojas, J. Mabey, Generation of curvilinear coordinates on multiply connected regions with boundary-singularities, J. Comput. Phys. 223 (2007) 571-588] to domains with a finite number of holes. Regions with multiple holes are reduced to several contiguous single hole subregions. Then, the BCGC algorithm is applied to each single hole subregion producing a smooth grid with line control. Finally, the subregions with their respective grids are joined and their interfaces are smoothed resulting a globally smooth grid. The advantages of the novel grids are revealed by employing them to numerically solve acoustic scattering problems in the presence of multiple complexly shaped obstacles.
Journal of Computational Physics, 2010
The applicability of the Dirichlet-to-Neumann technique coupled with finite difference methods is... more The applicability of the Dirichlet-to-Neumann technique coupled with finite difference methods is enhanced by extending it to multiple scattering from obstacles of arbitrary shape. The original boundary value problem (BVP) for the multiple scattering problem is reformulated as an interface BVP. A heterogenous medium with variable physical properties in the vicinity of the obstacles is considered. A rigorous proof of the equivalence between these two problems for smooth interfaces in two and three dimensions for any finite number of obstacles is given. The problem is written in terms of generalized curvilinear coordinates inside the computational region. Then, novel elliptic grids conforming to complex geometrical configurations of several two-dimensional obstacles are constructed and approximations of the scattered field supported by them are obtained. The numerical method developed is validated by comparing the approximate and exact far-field patterns for the scattering from two circular obstacles. In this case, for a second order finite difference scheme, a second order convergence of the numerical solution to the exact solution is easily verified.
El argumento de la habitación china y la teoría computacional de la mente
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Papers by Sebastian Acosta