Acoustic and elastic numerical wave simulations by recursive spatial derivative operators

A new scheme for the calculation of spatial derivatives has been developed. The technique is based on recursive derivative operators that are generated by an [Formula: see text] fit in the spectral domain. The use of recursive operators enables us to extend acoustic and elastic wave simulations to shorter wavelengths. The method is applied to the numerical solution of the 2D acoustic wave equation and to the solution of the equations of 2D dynamic elasticity in an isotropic medium. An example of reverse-time migration of a synthetic data set shows that the numerical dispersion can be significantly reduced with respect to schemes that are based on finite differences. The method is tested for the solutions of the equations of dynamic elasticity by comparing numerical and analytic solutions to Lamb’s problem.

DATA ALLOCATION STRATEGIES FOR PARALLEL IMAGE PROCESSING ALGORITHMS

This paper discusses several data allocation strategies used for the parallel implementation of basic imaging operators. It shows that depending on the operator (sequential or parallel, with regular or irregular execution time), the image data must be partitioned in very different manners: The square sub-domains are best adapted for minimizing the communication volume, but rectangles can perform better when we take into account the time for constructing messages. Block allocations are well adapted for inherently parallel operators since they minimize interprocessor interactions, but in the case of recursive operators, they lead to nearly sequential executions. In this framework, we show the usefulness of block-cyclic allocations. Finally, we illustrate the fact that allocating the same amount of image data to each processor can lead to severe load imbalance in the case of some operators with data-dependant execution times.

Creativeness and completeness in recursion categories of partial recursive operators

Recursion categories have been proposed by Di Paola and Heller in [DPH] as the basis for a category-theoretic approach to recursion theory, in the context of a more general and ambitious project of a purely algebraic treatment of incompleteness phenomena. The way in which the classical notion of creative set is rendered in this new category-theoretic framework plays, therefore, a central role. This is done in [DPH] (Definition 8.1) by defining the notion of creative domains or, rather, domains which are creative relative to some criterion: thus, in a recursion category, every criterion provides a notion of creativeness.A basic result on creative domains (cf. [DPH, Theorem 8.13]) is that, under certain assumptions, a version of the classical result, due to Myhill [MYH], stating that every creative set is complete, holds: in a recursion category with equality (i.e. exists for every object X) and having enough atoms, every domain which is creative with respect to atoms is also complete.