论文标题
球形帽的部分微分方程的稀疏光谱方法
Sparse spectral methods for partial differential equations on spherical caps
论文作者
论文摘要
近年来，使用经典正交多项式的层次结构得出了用于求解部分微分方程的稀疏光谱方法。在这项工作中，我们将方法扩展到球形帽上非古典多元正交多项式的层次结构。可以使用公式（非经典）单变量正交多项式来有效地计算部分差分运算符的离散分配。我们证明了涉及球形拉普拉斯和双旋转算子的部分微分方程的结果，显示了光谱收敛。
In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the methodology to a hierarchy of non-classical multivariate orthogonal polynomials on spherical caps. The entries of discretisations of partial differential operators can be effectively computed using formulae in terms of (non-classical) univariate orthogonal polynomials. We demonstrate the results on partial differential equations involving the spherical Laplacian and biharmonic operators, showing spectral convergence.
