printer friendly pageCME 206: Introduction to Numerical Methods for Engineering (ME 300C)
Numerical methods from a user's point of view. Lagrange interpolation, splines. Integration: trapezoid, Romberg, Gauss, adaptive quadrature; numerical solution of ordinary differential equations: explicit and implicit methods, multistep methods, Runge-Kutta and predictor-corrector methods, boundary value problems, eigenvalue problems; systems of differential equations, stiffness. Emphasis is on analysis of numerical methods for accuracy, stability, and convergence. Introduction to numerical solutions of partial differential equations; Von Neumann stability analysis; alternating direction implicit methods and nonlinear equations. Prerequisites:
CME 200/
ME 300A,
CME 204/
ME 300B.
Terms: Aut, Spr
| Units: 3
CME 207: Numerical Methods in Engineering and Applied Sciences (AA 214A, GEOPHYS 217)
Scientific computing and numerical analysis for physical sciences and engineering. Advanced version of CME206 that, apart from CME206 material, includes nonlinear PDEs, multidimensional interpolation and integration and an extended discussion of stability for initial boundary value problems. Recommended for students who have some prior numerical analysis experience. Topics include: 1D and multi-D interpolation, numerical integration in 1D and multi-D including adaptive quadrature, numerical solutions of ordinary differential equations (ODEs) including stability, numerical solutions of 1D and multi-D linear and nonlinear partial differential equations (PDEs) including concepts of stability and accuracy. Prerequisites: linear algebra, introductory numerical analysis (
CME 108 or equivalent).
Terms: Aut
| Units: 3
CME 211: Software Development for Scientists and Engineers (EARTH 211)
Basic usage of the Python and C/C++ programming languages are introduced and used to solve representative computational problems from various science and engineering disciplines. Software design principles including time and space complexity analysis, data structures, object-oriented design, decomposition, encapsulation, and modularity are emphasized. Usage of campus wide Linux compute resources: login, file system navigation, editing files, compiling and linking, file transfer, etc. Versioning and revision control, software build utilities, and the LaTeX typesetting software are introduced and used to help complete programming assignments. Prerequisite: introductory programming course equivalent to
CS 106A or instructor consent.
Terms: Aut
| Units: 3
Instructors:
Henderson, N. (PI)
;
Bear Don't Walk, O. (TA)
;
Indra Ramaswamy, S. (TA)
...
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Instructors:
Henderson, N. (PI)
;
Bear Don't Walk, O. (TA)
;
Indra Ramaswamy, S. (TA)
;
Janssen, L. (TA)
;
Nixon, E. (TA)
;
Romero, J. (TA)
CME 212: Advanced Programming for Scientists and Engineers (ENERGY 212)
Advanced topics in software development, debugging, and performance optimization are covered. The capabilities and usage of common libraries and frameworks such as BLAS, LAPACK, FFT, PETSc, and MKL/ACML are reviewed. Computer representation of integer and floating point numbers, and interoperability between C/C++ and Fortran is described. More advanced software engineering topics including: representing data in files, signals, unit and regression testing, and build automation. The use of debugging tools including static analysis, gdb, and Valgrind are introduced. An introduction to computer architecture covering processors, memory hierarchy, storage, and networking provides a foundation for understanding software performance. Profiles generated using gprof and perf are used to help guide the performance optimization process. Computational problems from various science and engineering disciplines will be used in assignments. Prerequisites:
CME 200 /
ME 300A and
CME 211. The
CME 211 requirement may be satisfied by passing a placement test administered by ICME.
Terms: Win
| Units: 3
Instructors:
Henderson, N. (PI)
;
Indra Ramaswamy, S. (TA)
;
Janssen, L. (TA)
...
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Instructors:
Henderson, N. (PI)
;
Indra Ramaswamy, S. (TA)
;
Janssen, L. (TA)
;
Kasera, R. (TA)
;
Romero, J. (TA)
CME 213: Introduction to parallel computing using MPI, openMP, and CUDA (ME 339)
This class will give hands on experience with programming multicore processors, graphics processing units (GPU), and parallel computers. Focus will be on the message passing interface (MPI, parallel clusters) and the compute unified device architecture (CUDA, GPU). Topics will include: network topologies, modeling communication times, collective communication operations, parallel efficiency, MPI, dense linear algebra using MPI. Symmetric multiprocessing (SMP), pthreads, openMP. CUDA, combining MPI and CUDA, dense linear algebra using CUDA, sort, reduce and scan using CUDA. Pre-requisites include: C programming language and numerical algorithms (solution of differential equations, linear algebra, Fourier transforms).
Terms: Spr
| Units: 3
CME 213B: Parallel Computing Projects
Students will discuss, devise and implement parallel applications for a discipline of mutual interest. The parallel implementation will focus on the use of MPI for clusters, OpenMP for multicore processors, and/or CUDA for GPU processors. Instructors will help guide students to relevant literature and resources. A short introduction to MPI, OpenMP, and CUDA will be given at the beginning of the quarter. Hardware will be available for the duration of the quarter including NVIDIA Jetson TK1 development kits, and the ICME GPU cluster. Prerequisites:
CME 211/212 or equivalent.
Last offered: Winter 2015
CME 214: Software Design in Modern Fortran for Scientists and Engineers (EARTH 214)
This course introduces software design and development in modern Fortran. Course covers the functional, object-oriented-, and parallel programming features introduced in the Fortran 95, 2003, and 2008 standards, respectively, in the context of numerical approximations to ordinary and partial differential equations; introduces object-oriented design and design schematics based on the Unified Modeling Language (UML) structure, behavior, and interaction diagrams; cover the basic use of several open-source tools for software building, testing, documentation generation, and revision control. Recommended: Familiarity with programming in Fortran 90, basic numerical analysis and linear algebra, or instructor approval
Terms: Aut
| Units: 3
CME 215A: Advanced Computational Fluid Dynamics (AA 215A)
High resolution schemes for capturing shock waves and contact discontinuities; upwinding and artificial diffusion; LED and TVD concepts; alternative flow splittings; numerical shock structure. Discretization of Euler and Navier Stokes equations on unstructured meshes; the relationship between finite volume and finite element methods. Time discretization; explicit and implicit schemes; acceleration of steady state calculations; residual averaging; math grid preconditioning. Automatic design; inverse problems and aerodynamic shape optimization via adjoint methods. Pre- or corequisite: 214B or equivalent.
Terms: Win
| Units: 3
Instructors:
Jameson, A. (PI)
CME 215B: Advanced Computational Fluid Dynamics (AA 215B)
High resolution schemes for capturing shock waves and contact discontinuities; upwinding and artificial diffusion; LED and TVD concepts; alternative flow splittings; numerical shock structure. Discretization of Euler and Navier Stokes equations on unstructured meshes; the relationship between finite volume and finite element methods. Time discretization; explicit and implicit schemes; acceleration of steady state calculations; residual averaging; math grid preconditioning. Automatic design; inverse problems and aerodynamic shape optimization via adjoint methods. Pre- or corequisite: 214B or equivalent.
Last offered: Spring 2012
CME 232: Introduction to Computational Mechanics (ME 332)
Provides an introductory overview of modern computational methods for problems arising primarily in mechanics of solids and is intended for students from various engineering disciplines. The course reviews the basic theory of linear solid mechanics and introduces students to the important concept of variational forms, including the principle of minimum potential energy and the principles of virtual work. Specific model problems that will be considered include deformation of bars, beams and membranes, plates, and problems in plane elasticity (plane stress, plane strain, axisymmetric elasticity). The variational forms of these problems are used as the starting point for developing the finite element method (FEM) and boundary element method (BEM) approaches providing an important connection between mechanics and computational methods.
Last offered: Summer 2015
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