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Konrad-Zuse-Zentrum fur Informationstechnik Berlin
 

Summary: Konrad-Zuse-Zentrum
fu¨r Informationstechnik Berlin
Takustraße 7
D-14195 Berlin-Dahlem
Germany
A CHIM S CHADLE M ARIA L OPEZ -F ERNANDEZ"
CHRISTIAN LUBICH**
Fast and oblivious convolution quadrature
^Departamento de Matem´atica Aplicada, Universidad de Valladolid.
"Mathematisches Institut, Universit¨at Tu¨bingen.
ZIB-Report 05-09 (January 2005)
FAST AND OBLIVIOUS CONVOLUTION QUADRATURE
ACHIM SCHADLE*, MARIA LOPEZ-FERNANDEZ^, AND CHRISTIAN LUBICH**
Abstract. We give an algorithm to compute N steps of a convolution quadrature approximation
to a continuous temporal convolution using only O(N logN) multiplications and O(logN) active
memory. The method does not require evaluations of the convolution kernel, but instead O(logN)
evaluations of its Laplace transform, which is assumed sectorial. The algorithm can be used for the
stable numerical solution with quasi-optimal complexity of linear and nonlinear integral and integro-
differential equations of convolution type. In a numerical example we apply it to solve a subdiffusion
equation with transparent boundary conditions.

  

Source: Andrzejak, Artur - Konrad-Zuse-Zentrum für Informationstechnik Berlin

 

Collections: Computer Technologies and Information Sciences