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Adaptive Calculation of Variable Coefficients Elliptic Differential Equations via Wavelets
 

Summary: Adaptive Calculation of Variable Coefficients
Elliptic Differential Equations via Wavelets
Amir Averbuch1
, Leonid Beliak2
, Moshe Israeli2
1
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978
Israel
2
Faculty of Computer Science, Technion- Israel Institute of Technology
Haifa 32000, Israel
Abstract
We propose a solver for 1-D strictly elliptic linear PDE's with non-con-
stant coefficients of the form U - b(x)U = f(x). We combine a sparse
multiplication algorithm with a diagonally preconditioned conjugate gradient
(CG) method. We use sparse data structures to take advantage of the O(Ns)
complexity of the algorithm, where Ns is the number of significant coefficients
(i.e. above a certain threshold) required for a given accuracy.
We show that the usage of a sparse multiplication in wavelet space rather
than in the original physical space can speed up the performance of the sparse

  

Source: Averbuch, Amir - School of Computer Science, Tel Aviv University

 

Collections: Computer Technologies and Information Sciences