Abstract
Trying to capture the essential physics of a natural phenomenon directly on computers may lead us to useful numerical schemes to solve the partial differential equation describing the phenomenon. Here we try to capture the consequences of space-time translational symmetry such as advection in fluids or Huygens’ principle in wave propagation. Efficient modeling of these phenomena becomes possible with the aid of Hermite polynomial interpolations to realize a continuum on discrete lattices. To illustrate these ideas, we present a new method to derive wave equation solvers that are high order but local (the computational cell or stencil includes nearest neighbors only), a clear advantage over standard high-order algorithms of the finite-difference or finite-element families. The purpose of the paper is to demonstrate our methodology. Therefore, in two- and three-spaces, details are given only for the lowest-order algorithms, a preview of a more optimal higher-order scheme is also included.
Original language | English (US) |
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Pages (from-to) | 4795-4810 |
Number of pages | 16 |
Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |
Volume | 57 |
Issue number | 4 |
DOIs | |
State | Published - 1998 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics