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Recent documents in Mathematics Thesesen-usSat, 21 May 2016 01:39:09 PDT3600The Numerical Solution of the Helmholtz Equation for the Bloodcell Shape: Mars Project
http://docs.rwu.edu/math_theses/2
http://docs.rwu.edu/math_theses/2Thu, 19 May 2016 06:22:59 PDT
The objective of this research is to investigate numerical solutions of several boundary value problems for the Helmholtz equation for the shape of a Biconcave Disk. The boundary value problems this research mainly focuses on are the Neumann and Robin boundary problems. The Biconcave Disk is a closed, simply connected, bounded shape modi ed from a sphere where the two sides concave toward the center, mapped by a sine curve. There are some numerical issues in this type of analysis; any integration is a ected by the wave number k, because of the oscillatory behavior of the fundamental solution of the Helmholtz equation. This project was funded by NASA RI Space Grant and the NASA EPSCoR Grant for testing of boundary conditions for the Biconcave Disk. This method has already been investigated for the sphere, ellipsoid, superellipsoid, and the oval of cassini. The primary purpose of this research is to extend those known results to the Biconcave Disk with calculating the possibility of this shape acquiring sucient conditions to be part of a spacecraft that might one day land on planet Mars.
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Jill Kelly ReshSolving the Helmholtz Equation for the Neumann Boundary Condition for the Pseudosphere by the Galerkin Method
http://docs.rwu.edu/math_theses/1
http://docs.rwu.edu/math_theses/1Thu, 12 May 2011 06:38:17 PDT
In this paper, the Helmholtz equation for the exterior Neumann boundary condition for the pseudosphere in three dimensions using the global Galerkin method is studied. The Galerkin method will be used to solve Jonesâ€™ modified integral equation approach (modified as a series of radiating waves will be added to the fundamental solution) for the Neumann problem for the Helmholtz equation, which uses a series of double sums to approximate the integral. A Fortran 77 program is used and some required subroutines from the Naval Warfare Center are called to help increase ouraccuracy since these boundary integrals are difficult to solve. The solutions obtained arecompared to the true solution for the Neumann problem to understand how well the method converges. The lower errors obtained show that the method for complete reflection of the sound waves off of the pseudosphere is accurate and successful. Also presented in this paper are both computational and theoretical details of the method ofdifferent values of k for the pseudosphere.
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Jane Pleskunas