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Hi my name is Ryan! I have degrees in Mathematics, Computer Science, and Engineering. My research interests are numerical analysis, partial differential equations and perturbation theory. I work for Dr. Zhilin Li. I do work related to Numerical Electromagnetics and IIM (Immersed Interface Method).

Great Wall Of Numerical Analysis - My Work

PhD Doctral Research - Dr. Zhilin Li. - Numerical Electrodynamics

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MA 531 Special Topics - PDE Optimization - Dr. Alen Alexanderian. - Numerical Variational Calculus

$ \begin{equation*} \begin{aligned} & \underset{f \in H^1[0,10]}{\text{minimize}} & & \int_{0}^{10} \sqrt{1+(f'(x))^2} dx \\ & \text{subject to} & f(0) =0 & & f(10) = 10 \end{aligned} \end{equation*}$

We solve the problem numerically taking a starting guess $f_o(x)=sin(x)$, we obtain convergence to the true answer, $f_{3000}(x) \approx x $. This is the true solution to the problem if we solved with the Euler-Lagrange Equations. Math is powerful

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MA 584 Finite Difference Method - Dr. Zhilin Li. - Wave Equation $u_{tt}=u_{xx}$

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MA 788 Numerical Methods for Conservation Laws - Dr. Pierre Gremaud. - Burgers Equation $u_{t} + uu_{x}=0 $ (very coarse grid)

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MA 587 Finite Element Method - Dr. Zhilin Li. - Laplaces Equation $u_{xx} + u_{yy}=0 $

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MATH 600 Spectral Methods - Dr. Michael Cromer (RIT) Heat Equation in 3D and 2D $u_{t}=u_{xx} + u_{yy} + u_{zz}$ and $u_{t}=u_{xx}+u_{yy}$

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Maxwells Equations

\begin{eqnarray} \nabla \cdot \vec{E} &=& \frac{\rho}{\epsilon_0}\\ \nabla \cdot \vec{B} &=& 0 \nonumber \\ \nabla \times \vec{E} &=& - \frac{\partial B}{\partial t} \nonumber \\ \nabla \times \vec{B} &=& \mu_{0}\vec{J} + \mu_{0}\epsilon_{0}\frac{\partial E}{\partial t} \end{eqnarray}

My First Result :High Resolution Godunov Method for Maxwell equations!

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  • M.S Operatirons Research NCSU 2017
  • B.S Mathematics RIT 2015
  • B.S Computer Science RIT 2015
  • A.S Engineering FLCC 2013
  • A.S Computer Science FLCC 2013
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