Musings of a Computational Philosopher
摘要
“Philosophy’s role is...to ask the right questions” (Slavoj Žižek), because there is little value in answering a misguided question. In this lecture I will try to ask the right questions concerning the correct computation of hyperbolic conservation laws. For example, I will argue that accuracy by itself is merely a low-frequency property of little value unless accompanied by bandwidth, robustness and stability. These properties are obtained by ensuring the correct flow of the correct information. The tools to achieve this are careful analysis of the governing equations and the use of appropriate stencils; several examples will be given. The approach throughout will be multidimensional. One dimensional analogies will be made only when appropriate. The recommendations that emerge are frequently not in accord with common practice.