A Second Order Finite-Difference Ghost-Point Method for Elasticity Problems on Unbounded Domains with Applications to Volcanology  

作　　者：Armando Coco Gilda Currenti Ciro Del Negro Giovanni Russo 

机构地区：[1]Dipartimento di Scienze della Terra e Geoambientali,Universita di Bari Aldo Moro,Bari,Italy. [2]Bristol University,Queens Road,Bristol BS81RJ,United Kingdom. [3]Istituto Nazionale di Geofisica e Vulcanologia,Italy. [4]Dipartimento di Matematica e Informatica,Universita di Catania,Catania,Italy

出　　处：《Communications in Computational Physics》2014年第9期983-1009,共27页计算物理通讯（英文）

基　　金：the OTRIONS project under the European Territorial Cooperation Programme Greece-Italy 2007-2013,and by PRIN 2009“Innovative numerical methods for hyperbolic problems with applications to fluid dynamics,kinetic theory and computational biology”.

摘　　要：We propose a finite-difference ghost-point approach for the numerical solution of Cauchy-Navier equations in linear elasticity problems on arbitrary unbounded domains.The technique is based on a smooth coordinate transformation,which maps an unbounded domain into a unit square.Arbitrary geometries are defined by suitable level-set functions.The equations are discretized by classical nine-point stencil on interior points,while boundary conditions and high order reconstructions are used to define the field variables at ghost-points,which are grid nodes external to the domain with a neighbor inside the domain.The linear system arising from such discretization is solved by a multigrid strategy.The approach is then applied to solve elasticity problems in volcanology for computing the displacement caused by pressure sources.The method is suitable to treat problems in which the geometry of the source often changes(explore the effects of different scenarios,or solve inverse problems in which the geometry itself is part of the unknown),since it does not require complex re-meshing when the geometry is modified.Several numerical tests are successfully performed,which asses the effectiveness of the present approach.

关 键 词：Linear elasticity Cauchy-Navier equations ground deformation unbounded domain coordinate transformation method Cartesian grid ghost points level-set methods multigrid. 

分 类 号：O17[理学—数学]