Especificação semântica de LaND: uma linguagem para o método das diferenças finitas

Abstract

Computer Science and Engineering (CSE) is a relatively new subject. It deals with applying and developing computer models and simulations, and it is often associated to high-performance computing. Using CSE methods effectively is currently an obstacle to engineers, due to their lack of specific training in algorithms, data structures, parallel programming and highperformance computing. Many artificial languages, either general or specific, have been recently developed: Matlab, Scilab and the numeric programming libraries Basic Linear Algebra Subprograms (BLAS), LINPACK, EISPACK, LAPACK and ScaLAPACK for instance. Generally, the engineer or scientist develops on their own a specific programming language, a software to meet their needs. The problem found within this process is the struggle transferred to the user as a consequence of these algorithms development. Besides the need to have total control over the problem and numeric method in question, they must deal with the development of the computer program implementing the algorithm for the problem resolution. The objective here is to present the formal semantic specifications for LaND - Language of Numerical Discretization, an artificial language able to reduce the complexity of scientific software development for problems involving Partial Differential Equations simulations with Finite Difference Methods. It is assumed the student, engineer or researcher only concern should be the inherent aspects of the solution within a certain problem, leaving the automatic generation of an equivalent program to the tool. This is a initial model proposal with focus on second-order hyperbolic problems with geometrically uniform computational mesh. Our approach is based on formal techniques of computing, such as denotational semantics, responsible for the mapping the mathematical objects in the numerical approximation model, giving meaning to these structures, and Communicating Sequential Processes (CSP), a formalism used to describe the communication patterns within the computational mesh.