General Scattered Field Simulator

An apparatus for simulating a physical response of a physical object to an incident field based on a computer-readable representation of the physical object, the apparatus comprising:

• one or more processors;
• and
• one or more memories operatively coupled to at least one of the one or more processors and having instructions stored thereon that, when executed by at least one of the one or more processors, cause at least one of the one or more processors to:
• access a patch data structure describing a surface of a scattering object, the patch data structure comprising more than one logically quadrilateral patches including a first patch, a second patch, and a third patch;
• access an incident field, a residual tolerance parameter, a proximity parameter, and a node numbers parameter;
• initialize a first mesh associated with the first patch, a second mesh associated with the second patch, and a third mesh associated with the third patch;
• determine, for a first node in the first mesh, that the second patch is a near patch based on the proximity parameter, the first approximation node in the first approximation mesh corresponding to a parametrization of the first point in the first patch;
• determine, for the first approximation node in the first mesh, a projection node in the second mesh;
• generate a self-patch contribution to a surface field component by at least:
• deforming, around the first approximation node in the first mesh, the first mesh by performing a first change of variables to obtain a first deformed mesh;
• generate for at least one first deformed node in the first deformed mesh a first respective product of discrete function approximators;
• and
• generate a near-patch contribution to the surface field component by at least:
• deforming, around the projection node in the second mesh, the second mesh by performing a second change of variables to obtain a second deformed mesh;
• generate for at least one second deformed node in the second deformed mesh a second respective product of discrete function approximators;
• and
• generate a far-patch contribution to the surface field component by integrating over the third patch;
• generate a plurality of surface field subcomponent approximation vectors based on the self-patch contribution, the near-patch contribution, and the far patch contribution;
• generate a surface field component based at least on surface field subcomponent approximation vectors;
• generate, when surface field component satisfies the residual tolerance, a scattered field based on a final density associated with a satisfied residual tolerance;
• and
• store the scattered field in a non-transitory data structure.

A computer implemented method for designing a computer model of a physical object, comprising:

• accessing a cad data structure describing a first design of a physical object;
• generating a set of reference patches comprising parametrization data, each reference patch of the set of reference patches corresponding to a surface patch of the cad data structure, the parametrization data logically associated with approximation nodes of an approximation mesh;
• for an approximation node of the approximation nodes precompute self-patch approximators based on a deformation change of variables;
• for an approximation node of the approximation nodes precompute near-patch approximators based on a deformation change of variables;
• generate self-patch approximator weights as a product of self-patch approximators and a kernel function and a Jacobian associated with the approximation node;
• store the near-patch and the self-patch approximator weights in a memory;
• generate an initial surface field component by:
• generating an initial density guess;
• generating far-patch contributions;
• accessing precomputed self-patch approximators and near-patch approximators from the memory;
• generate, based on the initial surface field component, an improved surface field component including an improved density;
• generate a residual of the improved surface field component based on an incident field;
• and
• generate, when the residual satisfies a residual tolerance parameter, a scattered field simulation of the incident field being scattered by the physical object,
• wherein the CAD data structure is modified based on the scattered field simulation to obtain a second design of the physical object.