Mesh-based numerical implementation of the localized boundary-domain integral-equation method to a variable-coefficient Neumann problem
Mesh-based numerical implementation of the localized boundary-domain integral-equation method to a variable-coefficient Neumann problem
复制标题
变系数诺依曼问题局部边界域积分方程法的基于网格的数值实现
DOI：
10.1007/s10665-004-6452-0
复制
发表时间：
2005
影响因子：
1.3
通讯作者：
I. Nakhova
中科院分区：
文献类型：
--
作者：
S. Mikhailov;I. Nakhova
摘要：讨论了用于二阶线性椭圆变系数偏微分方程的诺依曼边值问题数值求解的局部边界域积分方程（LBDIE）方法的实现。 LBDIE 方法使用专门构造的局部参数矩阵（Levi 函数）将 BVP 简化为 LBDIE。采用基于网格的离散化后，积分方程被简化为可数值求解的稀疏线性代数方程组。由于 Neumann BVP 不是无条件且唯一可解的，因此 LBDIE 也不是。还讨论了有限维扰动方法的数值实现，该方法将积分方程简化为无条件且唯一可解的方程。
Abstract.An implementation of the localized boundary-domain integral-equation (LBDIE) method for the numerical solution of the Neumann boundary-value problem for a second-order linear elliptic PDE with variable coefficient is discussed. The LBDIE method uses a specially constructed localized parametrix (Levi function) to reduce the BVP to a LBDIE. After employing a mesh-based discretization, the integral equation is reduced to a sparse system of linear algebraic equations that is solved numerically. Since the Neumann BVP is not unconditionally and uniquely solvable, neither is the LBDIE. Numerical implementation of the finite-dimensional perturbation approach that reduces the integral equation to an unconditionally and uniquely solvable equation, is also discussed.