三维外问题基于椭球面人工边界的区域分解法的开题报告摘要：三维外问题是地球物理勘探中的重要问题之一，区域分解法是求解三维外问题的一种重要方法。在本文中，我们提出基于椭球面人工边界的区域分解法，用于求解三维外问题。椭球面人工边界方法可以将复杂地质结构转化为一个简单的椭球形状，从而简化问题的处理。本文介绍了基于有限差分的数值模拟方法，以及用于求解边界值问题的迭代求解方法。我们还介绍了区域分解法的具体实现步骤，并通过数值实验来验证方法的正确性和可行性。关键词：三维外问题；椭球面人工边界；区域分解法；数值模拟；迭代求解Abstract:Three-dimensionalexternalproblemisoneoftheimportantproblemsingeophysicalexploration,anddomaindecompositionmethodisanimportantmethodforsolvingthree-dimensionalexternalproblems.Inthispaper,weproposedadomaindecompositionmethodbasedonellipticalartificialboundaryforsolvingthree-dimensionalexternalproblems.Theellipticalartificialboundarymethodcantransformcomplexgeologicalstructuresintoasimpleellipticalshape,therebysimplifyingtheproblem.Thispaperintroducesthefinitedifferencenumericalsimulationmethodandtheiterativesolutionmethodforsolvingboundaryvalueproblems.Wealsointroducethespecificimplementationstepsofthedomaindecompositionmethodandverifythecorrectnessandfeasibilityofthemethodthroughnumericalexperiments.Keywords:three-dimensionalexternalproblem;ellipticalartificialboundary;domaindecompositionmethod;numericalsimulation;iterativesolution