A spectral-infinite-element solution of Poisson's equation: an application to self gravity
A spectral-infinite-element solution of Poisson's equation: an application to self gravity
复制标题
泊松方程的谱无限元解：在自重力中的应用
DOI：
10.1111/j.1365-246x.2005.02711.x
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
J. Tromp
中科院分区：
文献类型：
--
作者：
H. N. Gharti;J. Tromp
本文将谱元法与映射无限元法相结合求解泊松方程。我们专注于地球静力学和地球动力学的问题，其中地球的引力场是由泊松方程在地球内部和拉普拉斯方程在其余的空间。谱元用于捕捉内场，无限元用于表示外场。为了求解Poisson/拉普拉斯方程的弱形式，我们在感兴趣区域内的谱元素中使用Gauss-Legendre-Lobatto求积。在区域外，我们在无限方向上使用Gauss-Radau求积，在其他方向上使用Gauss-Legendre-Lobatto求积。通过对均匀球体和参考地球模型（PREM）重力场的（半）解析解的比较，说明了该方法的有效性和准确性。
We solve Poisson's equation by combining a spectral-element method with a mapped infinite-element method. We focus on problems in geostatics and geodynamics, where Earth's gravitational field is determined by Poisson's equation inside the Earth and Laplace's equation in the rest of space. Spectral elements are used to capture the internal field, and infinite elements are used to represent the external field. To solve the weak form of Poisson/Laplace equation, we use Gauss-Legendre-Lobatto quadrature in spectral elements inside the domain of interest. Outside the domain, we use Gauss-Radau quadrature in the infinite direction, and Gauss-Legendre-Lobatto quadrature in the other directions. We illustrate the efficiency and accuracy of the method by comparing the gravitational fields of a homogeneous sphere and the Preliminary Reference Earth Model (PREM) with (semi-)analytical solutions.