Numerical Methods for Singularly Perturbed Differential Equations withApplications

摘要

During this one-year project, we continued our research on the development,analysis, and application of serial and parallel adaptive computational strategies for solving transient and steady partial differential systems. We concentrated on high-order methods and adaptive approaches that unite mesh refinement and coarsening (h-refinement), order variation (p-refinement), and mesh motion (r-refinement). Parallel computational techniques involved load-balancing and load-redistribution strategies for implementing these adaptive methods on distributed-memory MIMD computers. In particular, we have developed migration strategies that exchange finite elements between neighboring spatial domains of different processors. Effective load balancing in an adaptive setting requires speedy procedures since balancing must be performed frequently. Migration offers several advantages in this regard since it (i) has a low unit cost, (ii) can take advantage of locality, and (iii) can improve communications volumes. Procedures tested in two dimensional situations are being extended to three dimensions and preliminary methods, Singularly perturbed equations, Partial differential equations, Parallel computation.