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In three-dimensional problems, there are several forms for the surface integral:

 

1. Integrals over extrusion surfaces are selected by surface name or number and qualifying region name or number:

 

SINTEGRAL ( integrand, surface, region )

SURF_INTEGRAL ( integrand, surface, region )

 

If region is omitted, the integral is taken over all regions of the specified surface.  

If both surface and region are omitted, the integral is taken over the entire outer surface of the domain.  

 

Integrals of this type may be further qualified by selecting the layer in which the evaluation is to be made:

 

SURF_INTEGRAL ( integrand, surface, region, layer )

 

layer must be one of the layers bounded by the selected surface.

 

 

2. Integrals over "sidewall" surfaces are selected by boundary name and qualifying layer name:

 

SINTEGRAL ( integrand, named_boundary, named_layer )

SURF_INTEGRAL ( integrand, named_boundary, named_layer )

 

If layer is omitted, the integral is taken over all layers of the specified surface.    

 

Integrals of this type may be further qualified by selecting the region in which the evaluation is to be made:

 

SURF_INTEGRAL( integrand, named_boundary, named_layer, named_region )

 

named_region must be one of the regions bounded by the selected surface.

 

 

 

3. Integrals over entire bounding surfaces of selected subregions are selected by region name and layer name, as with volume integrals:

 

SINTEGRAL ( integrand, named_region, named_layer )

SURF_INTEGRAL ( integrand, named_region, named_layer )

 

If named_layer is omitted, the integral is taken over all layers of the specified surface.