论文标题
实际上单数方程的代码验证
Code Verification for Practically Singular Equations
论文作者
论文摘要
电场积分方程（EFIE）的实施方法实现，由于数值误差的各种来源及其可能的相互作用，因此引起了许多代码验证挑战。奇异积分使事物更加复杂，这是由于绿色功能的存在而引起的。为了解决这些奇异积分，以前提出了一种方法，其中解决方案和绿色的功能都是制造的。由于出现的方程式条件较差，因此将它们重新构成作为优化问题的一组约束，该问题选择了最接近生产解决方案的解决方案。在本文中，我们演示了对于这种实际奇异的方程式系统，如何通过将精确解决方案插入离散的方程式来计算截断误差无法检测到编码错误的某些顺序。另一方面，最佳解决方案的离散误差是一个更敏感的度量标准，它可以检测到比预期收敛速率的订单少。
The method-of-moments implementation of the electric-field integral equation (EFIE) yields many code-verification challenges due to the various sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. To address these singular integrals, an approach was previously presented wherein both the solution and Green's function are manufactured. Because the arising equations are poorly conditioned, they are reformulated as a set of constraints for an optimization problem that selects the solution closest to the manufactured solution. In this paper, we demonstrate how, for such practically singular systems of equations, computing the truncation error by inserting the exact solution into the discretized equations cannot detect certain orders of coding errors. On the other hand, the discretization error from the optimal solution is a more sensitive metric that can detect orders less than those of the expected convergence rate.
