A Compact Fourth Order Scheme for the Helmholtz Equation in Polar Coordinates

Abstract  In many problems, one wishes to solve the Helmholtz equation in cylindrical or spherical coordinates which introduces variable
coefficients within the differentiated terms. Fourth order accurate methods are desirable to reduce pollution and dispersion
errors and so alleviate the points-per-wavelength constraint. However, the variable coefficients renders existing fourth order
finite difference methods inapplicable. We develop a new compact scheme that is provably fourth order accurate even for these
problems. The resulting system of finite difference equations is solved by a separation of variables technique based on the
FFT. Moreover, in the r direction the unbounded domain is replaced by a finite domain, and an exact artificial boundary condition is specified as
a closure. This global boundary condition fits naturally into the inversion of the linear system. We present numerical results
that corroborate the fourth order convergence rate for several scattering problems.

• Content Type Journal Article
• DOI 10.1007/s10915-010-9348-3
• Authors
  
  
  • S. Britt, North Carolina State University Department of Mathematics Box 8205 Raleigh NC 27695 USA
  • S. Tsynkov, North Carolina State University Department of Mathematics Box 8205 Raleigh NC 27695 USA
  • E. Turkel, Tel Aviv University School of Mathematical Sciences Ramat Aviv Tel Aviv 69978 Israel
  
  

• Journal Journal of Scientific Computing
• Online ISSN 1573-7691
• Print ISSN 0885-7474

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Original source : http://www.springerlink.com/content/w36l4t65857v5n...