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The Ontario Research Centre for Computer Algebra
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Abstract: Supercomputing applications usually involve the repeated parallel application of discretized differential operators. Difficulties arise with higher-order discretizations their communications can overlap processors in complex ways. Their correct and efficient implementation requires careful choreography of computation and communication, taking into account the symmetries of the problem and of the computer's communication network. This paper shows how these symmetries can be used to automate the construction of the code for optimized operator computation. This is done with considerable generality by making the symmetries both of the problem and the computer explicit using the language of finitely presented reflection (Coxeter) groups, and using coset enumeration to generate and optimize the required code.
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