Modern computational mechanics: mappings and iterative methods; stability; convergence; consistency; numerical and symbolic solutions of ordinary and partial differential equations; finite-difference methods; the finite-element method; spectral methods. Applications to problems in solid mechanics, fluid mechanics, and dynamics. Same as CSE 450. 3 undergraduate hours. 3 or 4 graduate hours. Graduate students receive 4 graduate hours credit upon successful completion of an additional computational project. Prerequisite: MATH 285 or MATH 441; CS 101.
Introduction to computational mechanics
Problems, history, methodology (3 hr)
The nature of computational solid and fluid mechanics (6 hr)
Computations as mappings: theory, numerical experiments, physical interpretation (6 hr)
Ordinary differential equations arising in mechanics
Basic theory and numerical methods (3 hr)
Examples from solid and fluid mechanics, such as similarity solutions, systems with a finite number of modes; particle systems; vibrations; Lagrangian and Hamiltonian dynamics (6 hr)
Partial differential equations arising in mechanics
Finite-difference methods; discussion of the simplest advection equation; physical interpretation of consistency and stability; shocks; numerical and physical diffusion; stability and accuracy; diffusion equations, Burgers equation; wave equation; others (6 hr)
Functional expansions: Spectral methods; Fourier transformation, theory and numerical implementation; Burgers equation; convolution turns; de-aliasing; Navier-Stokes equation in a periodic box (2D and 3D); split-step method for nonlinear Schr|ouml;dinger equation; sample calculations (5 hr)
Functional expansions: Finite-element methods; examples (5 hr)
Introduction to other topics, e.g. particle methods, symbolic computing (5 hr)
TOTAL HOURS: 45
ME: MechSE or technical elective.