Multilevel Compression of Linear Operators
Descendants of Fast Multipole Methods (FMMs)
and Calderón-Zygmund Theory
Logistics and Syllabus: Yale, Fall 2013 Semester
Catalog number:
AMTH 510
Instructor:
Mark Tygert
Location:
Room 215, Leet Oliver Memorial (LOM) Hall, 12 Hillhouse Avenue
Times:
2:30 P.M. to 3:45 P.M. Mondays and Wednesdays
Grading:
If you take the course for credit,
your grade will be determined wholly by a "chat" with the instructor
at the end of the course.
Syllabus:
-
Volume and boundary integral equations
- Laplace equation
- Yukawa/screened-Coulomb/modified-Helmholtz equation
- Bi-Laplace equation
- Time-dependent wave equation
and scalar-Helmholtz/time-harmonic-wave equation
- Time-dependent Maxwell equations
and vector-Helmholtz/time-harmonic-Maxwell equations
- Applications in classical mechanics:
electro- and magnetostatics,
elasticity theory and very low-Reynolds-number fluid dynamics,
acoustics,
electrodynamics,
many-body dynamics,
and dynamics on lattices and in spherical coordinates
-
Iterative/not-locally-adaptive solution techniques
- Simplest/stationary: Neumann/Born series and Chebyshev approximations
- Krylov-subspace-based/non-stationary:
Generalized Minimum RESidual (GMRES)
and Conjugate Gradient (CG) methods
-
Numerical representations of function spaces and linear operators
based on algebra
- Singular Value Decompositions (SVDs)
- Interpolative Decompositions (IDs)
-
Fast methods for applying non-oscillatory linear integral operators
- Numerical representations based on algebra
- Numerical representations based on exponentials/plane-waves
-
Fast methods for applying the Green operators of time-harmonic wave equations
- Bessel functions and partial wave expansions
- Low frequency
- High frequency
- Wideband
- Directional/windowed translation operators
-
Fast Plane-Wave Time-Domain (PWTD) algorithm for the solution
of time-dependent wave equations
-
Direct/locally-adaptive solution techniques