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During the course of my graduate studies and after I have had many opportunities to apply Boundary Integral Equation Methods in the development of software for the analysis of various physical problems, including both subsonic and supersonic aerodynamics, free-surface hydrodynamics, macromolecular electrostatics and diffusion. All of these models employ a direct form of the integral representation based on the Greenīs function of the operator of interest, therefore the linear model requires only surface elements. Nonlinear problems are accessible at the cost of introducing a discretized field of sources. Recently my research concerns have been in applying BEM to macromolecular reaction kinetics: a continuum model, wherein the governing equations are both nonlinear and parabolic. The stochastic molecular motion is biased by electrostatic field potential and itsī gradient, for which integral formulations have already been implemented. If frequency domain is of interest, little modification would be required to produce a standard Helmholtz representation (much like the one for acoustics), since the screened exterior field is governed by a modified Helmholtz equation. In addition to the scalar formulation, I've the gradient of the scalar field: with proper finite part, these hypersingular integrals could be a useful component in the type of combined integral formulation necessary to avoid singularity problems inherent in the integral representation of the Helmholtz scattering problem. For time-domain problems, the compressible aerodynamic formulations are complete with retarded scalar potentials.
Many of the BEM formulations outlined above and in the accompanying letter have been developed to an industrial level and can be made available as design tools or platforms for further development.
Although my PhD is essentially in computational aerodynamics, Iīve a long interest in computing architectures, especially parallel applied to computational problems. To this end Iīve pursued a masters in computer engineering (see resume below).
I would welcome any opportunity to work on the development of algorithms for the approximation of partial differential governing aero, fluid, or molecular dynamics. Although the greater part of my professional activity has been occupied by the formulation and implementation of Galerkin methods, Iīve much academic interest in and exposure to numerical models of various types: differencing, multigrid, etc., as well as theoretical aspects of physical models of continua. Opportunities that allow exposure to new physics, numerical methods, and architectures are always greeted enthusiastically. Attached please find a brief description my recent research activities and my formal resume. I have just returned to the US. As I have no current contractual obligations, my availability is immediate. Thanks.
(NB: I also have files immediately available the abstract and introduction of the two most recent papers in preparation: the first one describes an algorithm that employs a set of recursive equations to compute arbitrarily higher order integrals required in the screened electrostatics problem, and the second one is the electrostatics integral formulation, itīs discretization and solution. Excerpts from other papers may be found below.)
Downey, Mark J., An Recursive Algorithm for the Evaluation of the Gradient Source and Doublet Integrals of Arbitrary Order for the Helmholtz Operator , (in preparation).
Downey, M. J., Calcagno, G., and Morino, L., Free-wake Analysis for Helicopters in Hover and Forward Flight , (in preparation).
Downey, M. J., Tseng, K., and Morino, L., A First-Order BEM for Supersonic Aeroelastic Problems , (in preparation).
Downey, M. J., Supersonic MODAIR: Theoretical Manual, Supersonic MODAIR: Users Manual, Supersonic MODAIR: Applications Manual, prepared for Alenia under contract BSRM93.
Downey, M. J., Higher Order Boundary Element Methods in Subsonic and Supersonic Aerodynamics , PhD Thesis, Boston University College of Engineering, 1995.
Downey, M. J., Morino, L., A Recursive Algorithm for the Evaluation of Arbitrary Source and Doublet Distributions , International Conference on Computational Engineering Science, April 10-14, 1988, Atlanta, GA, USA.
Downey, M. J., Boundary Element Methods on Parallel Machines , CCAD-TN-87-01.
Downey, M. J., Morino, L., A Higher-Order Boundary Element Formulation in Aerodynamics , CCAD-TR-86-01.
Other research interests include: high-speed parallel and specialized computer architectures, aspects of existence and uniqueness in integral equation methods, application of the theory of distributions in the formulation of problems in mathematical physics.
SUNDRY: US citizen, born in Elkhart, Indiana, USA, Languages: mother-tongue English, fluent Italian, survival Spanish and French. Interests: mountaineering, karate, and saxophone.
REFERENCES: available on request