Study presented in this paper is focused on comparison and statistical assessment of differences between the selected Level 2 products satellite mission Gravity Recovery Climate Experiment (GRACE). Global monthly gravity field models terms spherical harmonic coefficients produced by three institutes GRACE Science Data System are compared with partially independent MASCON global model. Detailed ...

We give a method of decomposing bundle-valued polynomials compatible with the action of the Lie group Spin(n), where important tools are Spin(n)-equivariant operators and their spectral decompositions. In particular, the top irreducible component is realized as an intersection of kernels of these operators. 0 Introduction Spherical harmonic polynomials or spherical harmonics are polynomial solu...

We develop in this paper an efficient and robust spectral-Galerkin method to solve the three-dimensional time-harmonic Maxwell equations in exterior domains. We first reduce the problem to a bounded domain by using the capacity operator which characterizes the nonreflecting boundary condition. Then, we adapt the transformed field expansion (TFE) approach to reduce the problem to a sequence of M...

A novel derivation, involving the Fourier transform and the addition theorem of harmonic polynomials, is presented for multi-centre molecular integrals over spherical Gaussiantype orbitals. Compact closed-form formulae, consisting of vector-coupling coefficients and well known functions only, are obtained for all multi-centre molecular integrals. The resulting formulae manifest the angular and ...

The problem of resolving spherical harmonic components from numerical data defined on a rectangular grid has many applications, particularly for the problem of gravitational radiation extraction. A novel method due to Misner improves on traditional techniques by avoiding the need to cover the sphere with a coordinate system appropriate to the grid geometry. This paper will discuss Misner’s meth...

A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to the treatment of boundary conditions imposed at radii larger than the size of the grid, following Abrahams, Rezzola, Rupright et al. [1]. In the method describ...

We accelerate the computation of spherical harmonic transforms, using what is known as the butterfly scheme. This provides a convenient alternative to the approach taken in the second paper from this series on “Fast algorithms for spherical harmonic expansions.” The requisite precomputations become manageable when organized as a “depth-first traversal” of the program’s control-flow graph, rathe...

In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention in numerical relativity over the past few years, especially as applied to the problem of binary inspiral and merger. A key issue when using the technique is t...