二维时谐波的全离散Calderón微积分
A fully discrete Calderon Calculus for two dimensional time harmonic waves
AI总结：
针对二维Helmholtz方程，提出一种基于交错网格的全离散Calderón微积分，通过Dirac delta分布和分段常数函数离散化，实现二阶收敛的数值格式。
摘要：
本文提出了二维Helmholtz方程的全离散Calderón微积分。该全离散化可以理解为高度非协调的Petrov-Galerkin方法，基于两个交错网格（网格尺寸$h$），用Dirac delta分布替代声学电荷密度，用分段常数函数近似声学偶极子密度。由此微积分得到的数值格式在连续方程适定情况下均具有$h^2$阶精度。最后，我们通过数值实验展示了该离散微积分的性能。
英文摘要：
In this paper, we present a fully discretized Calderón Calculus for the two dimensional Helmholtz equation. This full discretization can be understood as highly non-conforming Petrov-Galerkin methods, based on two staggered grids of mesh size $h$, Dirac delta distributions substituting acoustic charge densities and piecewise constant functions for approximating acoustic dipole densities. The resulting numerical schemes from this calculus are all of order $h^2$ provided that the continuous equations are well posed. We finish by presenting some numerical experiments illustrating the performance of this discrete calculus.
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