Mathematics ThesesCopyright (c) 2017 Roger Williams University All rights reserved.
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Recent documents in Mathematics Thesesen-usWed, 17 May 2017 01:36:37 PDT3600Numerical Solutions of the Radiosity Equation by the Galerkin Method for the Spherical Pyramid (Mars Project)
http://docs.rwu.edu/math_theses/4
http://docs.rwu.edu/math_theses/4Mon, 15 May 2017 06:39:29 PDT
The Radiosity of a surface is the rate at which energy leaves that surface. It includes the energy emitted by a surface as well as the energy reflected. In this thesis, a spherical shaped interior space was designed on a spacecraft, which one day might land on Mars. The Radiosity model was used to determine the brightness inside the space. A global Galerkin method is used to solve the Radiosity Equation for several spherical shapes. This research is based on the study of the Radiosity Equation for occluded surfaces using the Collocation Method by Atkinson and Chein. The previous research was done on the Sphere, Perturbation of the Sphere, Ellipsoid and the Oval of Cassini. The convergence errors between true solutions and approximated numerical solutions for different reflectivity values and emissivity functions were presented.
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Qiuyang DengThe Numerical Solution of the Exterior Impedance (Robin) Problem for the Helmholtzâ€™s Equation via Modified Galerkin Method: Superllipsoid
http://docs.rwu.edu/math_theses/3
http://docs.rwu.edu/math_theses/3Thu, 09 Jun 2016 11:49:42 PDT
This thesis focuses on finding the solution for the exterior Robin Problem for the Helmholtz Equation and therefore, determines how a convergent smooth surface depending on its outer shape, in this case the superellipsoid, responds to different outer waves. The primary purpose is to calculate the possibility of a certain object, acquiring sufficient conditions, to either submerge under respectively high water pressure or maintain in outer space; if applicable, this approach can be used for a new efficient design of a portion of a submarine or part of a space craft, the second of more interest to NASA, one of my sponsors. In this thesis, I analyze the numerical solution for the Helmholtz equation in 3 Dimensions, for the superellipsoid for the Robin Boundary Condition and answer the question of how a surface reacts to incoming waves approaching from various directions. Would the object tend to the extremes of either absorbing or reflecting everything with which it comes into contact, or would it obtain a neutral combination of the two.
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Hy DinhThe 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