TranAir Technology: Solutions for Large PDE Problems

TRANAIR is a series of computer codes for the solution of second order partial differential equations (PDEs) in three dimensions. The technology used in the TRANAIR codes can be viewed as a novel combination of boundary element methods and finite element field methods for the solution of three dimensional boundary value problems. This combination of techniques allows the solution of larger systems of equations than conventional boundary element or finite element techniques permit. TRANAIR codes have been applied to a wide variety of three dimensional computational problems which are purely elliptic (linear potential flow), problems which are elliptic but have embedded regions of hyperbolic character (the full potential equation, describing transonic flow) and indefinite elliptic problems (acoustic and electromagnetic scattering problems). Many applications have involved extremely complex and realistic geometries. Performance of the approach is very similar regardless of the type of problem. In this paper we discuss the TRANAIR technology in the context of its applications to the solution of large PDE problems.

[1]  R. Hockney.  The potential calculation and some applications , 1970 .

[2]  Aga M. Goodsell,et al.  TranAir and Euler computations of a generic fighter including comparisons with experimental data. [full-potential equations for transonic flow , 1989 .

[3]  D. Rose,et al.  Global approximate Newton methods , 1981 .

[4]  Hanan Samet,et al.  The Quadtree and Related Hierarchical Data Structures , 1984, CSUR.

[5]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[6]  R. Mittra,et al.  Transform approach to electromagnetic scattering , 1979, Proceedings of the IEEE.

[7]  D. P. Young,et al.  GMRES acceleration of computational fluid dynamics codes , 1985 .

[8]  John E. Bussoletti,et al.  Transonic analysis of arbitrary configurations using locally refined grids , 1989 .

[10]  Richard H. Burkhart,et al.  A new approach to the solution of boundary value problems involving complex configurations , 1986 .

[11]  Jack J. Dongarra,et al.  Solving banded systems on a parallel processor , 1987, Parallel Comput..

[12]  Richard H. Burkhart,et al.  TRANAIR - A computer code for transonic analyses of arbitrary configurations , 1987 .

[13]  O. Buneman.  Analytic inversion of the five-point poisson operator , 1971 .

[14]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[15]  Norbert N. Bojarski,et al.  K-Space Formulation of the Electromagnetic Scattering Problem , 1972 .

[16]  Gautam Sengupta,et al.  Numerical prediction of airborne noise transmission into a fuselage , 1987 .

[17]  D. P. Young,et al.  Application of sparse matrix solvers as effective preconditioners , 1989 .

[18]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[19]  J. Gillis,et al.  Methods in Computational Physics , 1964 .

[20]  R. A. James,et al.  The solution of Poisson''s equation for isolated source distributions , 1977 .