Polynomials over structured grids

Local Decoding and Testing of Polynomials over Grids

The well-known DeMillo-Lipton-Schwartz-Zippel lemma says that n-variate polynomials of total degree at most d over grids, i.e. sets of the form A1×A2×· · ·×An, form error-correcting codes (of distance at least 2−d provided mini{|Ai|} ≥ 2). In this work we explore their local decodability and local testability. While these aspects have been studied extensively when A1 = · · · = An = Fq are the s...

Tutte Polynomials in Square Grids

11 Composite Overset Structured Grids

The use of composite overset structured grids is an effective means of dealing with a wide variety of flow problems that spans virtually all engineering disciplines. Numerous examples involving steady and unsteady three-dimensional viscous flow for aerospace applications exist in the literature. The literature also chronicles a host of applications of the approach in areas as diverse as biomedi...

Chebyshev polynomials over finite fields and reversibility of -automata on square grids

Using number theory on function fields and algebraic number fields we prove results about Chebyshev polynomials over finite prime fields to investigate reversibility of two-dimensional additive cellular automata on finite square grids. For example, we show that there are infinitely many primitive irreversible additive cellular automata on square grids when the base field has order two or three.

Block-structured grids for Eulerian gyrokinetic simulations

In order to predict the turbulent transport in magnetic fusion experiments, global (i.e., full-torus) gyrokinetic simulations are often carried out. In this context, one frequently encounters situations in which the plasma temperature varies by large factors across the radial simulation domain. In grid-based Eulerian codes, this enforces the use of a very large number of grid points in the two-...