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Scalar PDE Coefficients

A scalar PDE is one of the following:

  • Elliptic

    (cu)+au=f.

  • Parabolic

    dut(cu)+au=f.

  • Hyperbolic

    d2ut2(cu)+au=f.

  • Eigenvalue

    (cu)+au=λdu.

In all cases, the coefficients d, c, a, and f can be functions of position (x and y) and the subdomain index. For all cases except eigenvalue, the coefficients can also depend on the solution u and its gradient. And for parabolic and hyperbolic equations, the coefficients can also depend on time.

The question is how to represent the coefficients for the toolbox.

There are three ways of representing each coefficient. You can use different ways for different coefficients.

For an example incorporating each way to represent coefficients, see Scalar PDE Functional Form and Calling Syntax.

    Note:   If any coefficient depends on time or on the solution u or its gradient, then that coefficient should be NaN when either time or the solution u is NaN. This is the way that solvers check to see if the equation depends on time or on the solution.

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