Abstract: Systems and methods for modeling physical systems include displaying geometric representation of a physical system on a physics simulation system. User-selection inputs received indicate, for mesh elements, selections of dependent variable shape function spaces representing dependent variables. Geometry shape function space options for simulating the physical system are determined that are common to mesh elements and include a serendipity shape function space of second order or higher. A determined geometry shape function space option is a subset of a combination of the dependent variable shape function spaces and satisfies accuracy criteria based on an accuracy ordering of shape function spaces. A finite element mesh for the physical system is created based on the mesh elements, a selected geometry shape function space, and the selection of dependent variable shape function spaces.

Abstract: A simulation apparatus for adding extra geometries to a model of a physical system. The apparatus is configured to modify a geometry of a model of a physical system represented in terms of a combined set of equations. Instructions on the apparatus cause one or more processors to perform, upon execution, acts comprising: (i) receiving a base geometry of the physical system, (ii) receiving one or more extra geometries associated with the base geometry, (iii) determining first geometric entities of the base geometry and second geometric entities of the extra geometry, (iv) adding the extra geometries to the base geometry by computing a product geometry of the determined first geometric entities and the second geometric entities, (v) generating an updated combined set of equations including representations of the product geometry, and (vi) generating a graphical representation of the product geometry, the graphical representation configured for display on the display device.

Abstract: A simulation apparatus for adding extra geometries to a model of a physical system. The apparatus is configured to modify a geometry of a model of a physical system represented in terms of a combined set of equations. Instructions on the apparatus cause one or more processors to perform, upon execution, acts comprising: (i) receiving a base geometry of the physical system, (ii) receiving one or more extra geometries associated with the base geometry, (iii) determining first geometric entities of the base geometry and second geometric entities of the extra geometry, (iv) adding the extra geometries to the base geometry by computing a product geometry of the determined first geometric entities and the second geometric entities, (v) generating an updated combined set of equations including representations of the product geometry, and (vi) generating a graphical representation of the product geometry, the graphical representation configured for display on the display device.

Abstract: A simulation apparatus for adding extra geometries to a model of a physical system. The apparatus is configured to modify a geometry of a model of a physical system represented in terms of a combined set of equations. Instructions on the apparatus cause one or more processors to perform, upon execution, acts comprising: (i) receiving a base geometry of the physical system, (ii) receiving one or more extra geometries associated with the base geometry, (iii) determining first geometric entities of the base geometry and second geometric entities of the extra geometry, (iv) adding the extra geometries to the base geometry by computing a product geometry of the determined first geometric entities and the second geometric entities, (v) generating an updated combined set of equations including representations of the product geometry, and (vi) generating a graphical representation of the product geometry, the graphical representation configured for display on the display device.