The Resolve Section

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The Resolve Section

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The RESOLVE section is used to define additional criteria for use by the adaptive regridder.  In the normal case, FlexPDE repeatedly refines the computational mesh until the estimated error in the approximation of the PDE's is less than the declared or default value of ERRLIM.  In some cases, this can be achieved with a much less dense mesh than is necessary to make pleasing graphical presentation of derived quantities, such as derivatives of the system variables, which are much less smooth than the variables themselves.  In the RESOLVE section, the user may declare one or more additional functions whose detailed resolution is important.  The section has the form:

RESOLVE  ( spec1 ) , ( spec2 ) , ( spec3 ) {...}


Here, each spec may be either an expression, such as "( shear_stress)",  or an expression followed by a weighting function, as in "(shear_stress, x^2)".


In the simplest form, only the expressions of interest need be presented.  In this case, for each stated function, FlexPDE will

form a Finite Element interpolation of the stated function over the computational mesh

find the deviation of  the interpolation from the exact function

split any cell where this deviation exceeds ERRLIM times the global RMS value of the function.


Because the finite element interpolation thus formed assumes continuous functions, application of RESOLVE to a discontinuous argument will result in dense gridding at the discontinuity.  An exception to this is at CONTACT boundaries, where the finite element representation is double valued.


In the weighted form, an importance-weighting function is defined, possibly to restrict the effective domain of resolution.  The splitting operation described above is modified to multiply the deviation at each point by the weight function at that point. Areas where the weight is small are therefore subjected to a less stringent accuracy requirement.



 Samples | Usage | Mesh_Control | Resolve.pde