Modeling, Analysis, and Computation of interesting scientific / technological / industrial problems

commonly known as

Prof. Vasilios ALEXIADES Ayres 213 974-4922 alexiades@utk.edu

8-10 Lab/Homework assignments: 40% , Project assignments: 40% , Term/Team Project: 20%

Contact the Office of Disability Services (2227 Dunford Hall, 974-6087) to coordinate reasonable accommodations for documented disabilities.

Involves: scientific problem → math problem → computational algorithm → numerical solution → implications for original scientific problem. CSE-HPC.jpg

It has become the 3rd pillar of Science, complementing Theory and Experiment.

Need to be solved numerically (approximately), so need

These aims often play against each other, so trade-offs need to be made...

The course will simulate the core aspects of
** Computational Science** including:
•

• writing reports • writing proposals • collaborating with colleagues on a Team/Term project • and presenting your work.

I.Crystal precipitation- physical model leading to ODE system - about ODEs - well posedness of IVP - equilibria - root finding (Newton method) - plotting - analysis of the model - Euler scheme - computational errors - consistency-stability-convergence - implementation - classical RK4 and other numerical schemes II.Air pollution: Advection and Diffusion Processes- the general conservation law u_{t}+ div F = 0 - derivation from first principles - conservation of species - advective and diffusive fluxes - continuity equation - constitutive laws (for non-advective fluxes) - finite volume discretization of u_{t}+ F_{x}= 0 - explicit/implicit - diffusion ( F = −Du_{x}) - parabolic PDEs - boundary conditions - explicit scheme - CFL condition - super-time-stepping acceleration - advection ( F = uV ) - explicit upwind scheme - CFL condition - implementation - linear advection - wave propagation - 1st order PDEs - method of characteristics - advection-diffusion ( F = uV − Du_{x}) - explicit scheme - CFL condition - effect of small/large Peclet number - a few words about Lax-Wendroff and other schemes III.Chemical reactionsvia mass action kinetics IV.Uncertainty Quantification and parameter estimationSome other possible topics: V.Melting and Freezing- phase-change basics, moving boundary problems - Stefan Problem, exact solution, analytic approximations - enthalpy formulation, explicit scheme VI.The catalytic converter- diffusion-reaction model - control problem - calculus of variations - Euler-Lagrange equation - numerical scheme for the forward model VII.Electron beam lithography(inverse problems) - forward scattering (dose to exposure) - inverse problem (exposure to dose) - ill posed problem - Fourier-Poisson integral solution of diffusion equation - Fourier series solution of diffusion equation - Fourier series approximation of the inverse problem - Discrete Fourier Transform, FFT

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