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## Mapping vector fields onto different domains

I am trying to develop a solution to a problem which consists of taking a given vector field (force) and converting that field from one domain to another while maintaining an equivalent system of forces. The real world problem occurs in posttensioning design where steel tendons are place in concrete members and then a tensile force is applied to the tendon, which is then restrained at the end points, creating a compressive vector field in the concrete. Typically, finite element methods are used to solve the problem which involve discretizing the physical members and solving the model; however you are constrained to developing the geometry of the model such that the elements defining the tendons must have nodes coincident with the concrete elements to maintain compatibility of displacements for the system. What I would like to do is separate the two models (domains) such that you can model the tendons and create a tendon vector field with points independent of the concrete elements and then develop a routine that will create an equivalent concrete vector field defined with a different set of points. This would allow the designer to develop the two models independent of each other and simply map the tendon forces onto the concrete elements through a mapping of one set of forces onto the other. The concept seems simple, but I am seeking some assistance in the implementation with Maple. Briefly stated, is there a standard solution technique to map one vector field onto another? The rub is that there is not a one-one correspondence for the coordinates. Thank you for your consideration of the problem.

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