Plenary Lecture

General Ray Method and Computer Program Package for Explicit Solution of Boundary Value Problems for Elliptic Partial Differential Equations in Domains with Complicated Geometry.

Professor Alexander Grebennikov
Faculty of Physical and Mathematical Sciences
Autonomous University of Puebla
Av. San Claudio y Río verde, Ciudad Universitaria,
CP 72570, Puebla
MÉXICO
E-Mail: agrebe@fcfm.buap.mx

Abstract: A new version of General Ray (GR) method for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. This version is based on application of the Radon transform directly to the PDE and consists in reduction PDE to assemblage of ODE. The class of the PDE includes the Laplace, Poisson and Helmgoltz equations. GR-method presents the solution of the Dirichlet boundary value problem for this type of equations by explicit analytical formulas that use the direct and inverse Radon transform. Proposed version of GR-method is justified theoretically, realized by fast algorithms and MATLAB software, which quality is demonstrated by numerical experiments.

Short Biography of the Speaker:
Grebennikov Alexander Ivanovich was born at 17 of April 1950 in Gorky city, Russia. The student of the Faculty of Calculating Mathematics and Cybernetics (FCMC) of Gorky State University at 1967-1972. Postgraduate student of the FCMC of Moscow State University (MSU) at 1972-1975. Was graduated PhD in 1976. Scientific interests: splines; data processing; inverse and ill-posed problems; fast algorithms in numerical analysis and applications. Publications: more than 120 articles in journals and proceedings, 2 texts of lectures, 5 monographs. Work: assistant professor of the FCMC MSU at 1976-1989; senior staff scientist of Scientific Research Computing Center (SRCC) MSU at 1989-1994; Head of Laboratory in SRCC MSU at 1995-1999; full professor of the Faculty of Physic and Mathematic Sciences of Autonomous University of Puebla, Mexico from 1999 to present day. Adres: Av. San Claudio y Río verde, Ciudad Universitaria, FCFM, CP 72570, Puebla, tel./fax (52 222) 8920073, e-mail: agrebe@fcfm.buap.mx