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- W181271750 abstract "Escript is a Python-based programming tool for modeling physical processes with a focus on Earth Sciences, seehttps://launchpad.net/Escript-finley. Users can easily implement complex models represented through strongly orloosely coupled partial differential equations (PDEs). Model scripts can be run on desktop computers as well aslarge scale parallel computers without any modifications. The key components in Escript are general linear PDEsand PDE coefficients which are both represented through appropriate Python classes. Users can combine instancesof these classes to build and couple mathematical models without the need to access the data structures used for thenumerical representation on the C/C++ level. Escript has been successfully applied to a broad variety of problemsincluding mantel convection, melting processes, volcanic flow, earthquakes, mineralization, plate subduction, andtsunamis.In many situations, e.g. when solving nonlinear PDEs using the Newton-Raphson scheme, solving inversion problems,or for sensitivity analysis, a linearization of the PDE is required. Due to the complexity of this operation it ishighly desirable that the calculation of the linearization is (completely or partially) automated. Computer algebraprovides an appropriate framework to perform this task. The focus of recent development work on Escript has beenthe introduction of symbolic representations of (nonlinear) PDEs and PDE coefficients allowing for automated calculationsof PDE linearizations with respect to the solution as well as PDE coefficients. The actual solution process(e.g. the Newton-Raphson iteration scheme to solve a nonlinear PDE) still requires the solution of a series of linearPDE which are solved numerically (e.g. using finite elements).In the paper we will present a concept of symbolical representation of PDEs for Escript outline its implementationfor Python and discuss some aspects of efficiency at the interface between symbolic and numerical calculations.We will illustrate the usage of this concept to solve an inversion problem for spatial variable PDE parameter." @default.
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- W181271750 date "2012-01-01" @default.
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- W181271750 title "Combining numerical and symbolic computing in Python" @default.
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