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Graph grammar and algorithmic transformations

Graph grammar and algorithmic transformations. Lecture topics: Generalization to 1D finite element method. GENERALIZATION TO 1D FINITE ELEMENT METHOD. Strong formulation. Find such that. Weak formulation. Find such that.

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Graph grammar and algorithmic transformations

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  1. Graph grammarand algorithmic transformations Lecture topics: Generalization to 1D finite element method

  2. GENERALIZATION TO 1D FINITE ELEMENT METHOD Strong formulation Find such that Weak formulation Find such that

  3. GENERALIZATION TO 1D FINITE ELEMENT METHOD Finite element method disretization Exemplary shape functions for [0,l] = [0,1], for two finite elements

  4. GENERALIZATION TO 1D FINITE ELEMENT METHOD Exemplary shape functions for [0,l] = [0,1], for two finite elements

  5. GENERALIZATION TO 1D FINITE ELEMENT METHOD Exemplary shape functions for [0,l] = [0,1], for two finite elements

  6. GENERALIZATION TO 1D FINITE ELEMENT METHOD Global shape functionsare composed with local shape functions, e.g. Local system of equations generated over the element K

  7. GENERALIZATION TO 1D FINITE ELEMENT METHOD Notice that when we switch from finite difference to finite elements, it only changes the local systems of equations at tree nodes

  8. GENERALIZATION TO 1D FINITE ELEMENT METHOD Notice that when we switch from finite difference to finite elements, it only changes the local systems of equations at tree nodes

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