A class of bases in L2 for the sparse representations of integral operators
SIAM Journal on Mathematical Analysis
Spectral methods on triangles and other domains
Journal of Scientific Computing
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We construct high-order mixed current vector basis (unctions on an arbitrary curved surface which can be subdivided as a union of curved triangles and quadrilaterals. The objective is to construct vector basis (a) which consists of high-order polynomials of the surface parameterization variables on triangles and quadrilaterals, (b) part of the basis will have vanishing moments on the triangles and quadrilaterals. The first property will enable us to represent the current distribution over scatter surface with much less number of unknowns and larger patches of either triangular or quadrilateral shapes. The second property will achieve what wavelet basis does on an interval, but on a more general domain, namely, a sparse matrix representation for some integral operators.