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The method is based on finite differences where the differentiation operators exhibit summation-by-parts properties. Typically, these operators consist of differentiation matrices with central difference stencils in the interior with carefully chosen one-sided boundary stencils designed to mimic integration-by-parts in the discrete setting.
A von Neumann architecture scheme. The von Neumann architecture—also known as the von Neumann model or Princeton architecture—is a computer architecture based on the First Draft of a Report on the EDVAC, [1] written by John von Neumann in 1945, describing designs discussed with John Mauchly and J. Presper Eckert at the University of Pennsylvania's Moore School of Electrical Engineering.
The terms "mesh generation," "grid generation," "meshing," " and "gridding," are often used interchangeably, although strictly speaking the latter two are broader and encompass mesh improvement: changing the mesh with the goal of increasing the speed or accuracy of the numerical calculations that will be performed over it.
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. [1]
A hybrid automaton is a finite-state machine with a finite set of continuous variables whose values are described by a set of ordinary differential equations. This combined specification of discrete and continuous behaviors enables dynamic systems that comprise both digital and analog components to be modeled and analyzed.
In theoretical computer science, a discrete system is a system with a countable number of states. Discrete systems may be contrasted with continuous systems, which may also be called analog systems. A final discrete system is often modeled with a directed graph and is analyzed for correctness and complexity according to computational theory.
Computer simulation is the running of a mathematical model on a computer, the model being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict.
MOOSE is designed to do everything else for the application developer, such as finite element discretization of the PDEs, the nonlinear solver, and the parallel high performance computing.