Apparatus and method for defining coupled systems on spatial dimensions and extra dimensions

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.

What is claimed is: 
     
         1 . A simulation method executed in a computer system with one or more processors configured to modify a geometry of a model of a physical system including physical quantities represented in terms of a combined set of equations, the simulation method comprising the acts of:
 defining geometry data representing a geometry of a physical system represented by a first combined set of equations, said geometry data associated with a first model of said physical system;   defining, via one or more processors, extra geometry data representing one or more extra geometries for a modified model based on said first model;   determining, via at least one of said one or more processors, a first set of geometric entity data representing one or more geometric entities of said geometry of said physical system from which to extend said one or more extra geometries;   adding, via at least one of said one or more processors, at least a portion of said extra geometry data representing at least one of said one or more extra geometries to said determined first set of geometric entity data representing one or more geometric entities by forming product geometry data representing a product geometry for said modified model, said extra geometry data representing said one or more extra geometries being at least a part of said product geometry data;   generating, via at least one of said one or more processors, non-discretized equation data representing a non-discretized second combined set of equations for at least a portion of said product geometry data; and   optionally generating a graphical representation of at least a portion of said product geometry data, said graphical representation configured for display on a graphical user interface.   
     
     
         2 . The method of  claim 1 , wherein said graphical representation includes said at least a portion of said product geometry data. 
     
     
         3 . The method of  claim 1 , wherein an extra dimension includes said one or more extra geometries. 
     
     
         4 . The method of  claim 1 , further comprising the act of:
 determining, via at least one of said one or more processors, a second set of geometric entity data representing one or more geometric entities of said one or more extra geometries; and   determining product selection data representing a product of selections computed as a Cartesian product between at least a portion of said first set of geometric entity data representing one or more geometric entities of said geometry and at least a portion of said second set of geometric entity data representing one or more geometric entities of said one or more extra geometries.   
     
     
         5 . The method of  claim 1 , wherein said non-discretized equation data representing said non-discretized second combined set of equations are user editable to allow editing of said second combined set of equations. 
     
     
         6 . The method of  claim 1 , wherein said non-discretized second combined set of equations are a combined set of non-discretized partial differential equations configured as input data for a partial differential equation solver. 
     
     
         7 . The method of  claim 1 , wherein at least one of said one or more geometric entities is a vertex. 
     
     
         8 . The method of  claim 1 , wherein at least one of said one or more geometric entities is an edge. 
     
     
         9 . The method of  claim 1 , wherein at least one of said one or more geometric entities is a boundary. 
     
     
         10 . The method of  claim 1 , wherein at least one of said one or more geometric entities is a domain. 
     
     
         11 . The method of  claim 1 , further comprising the act of defining material property data representing a material property for at least one of said one or more extra geometries. 
     
     
         12 . The method of  claim 1 , further comprising the act of:
 after forming said product geometry data representing said product geometry for said modified model, defining material property data representing a material property for at least a portion of said product geometry data.   
     
     
         13 . The method of  claim 1 , wherein said geometry of said physical system is one-dimensional and said one or more extra geometries are two-dimensional. 
     
     
         14 . The method of  claim 1 , wherein said geometry of said physical system is three-dimensional and said one or more extra geometries are one-dimensional. 
     
     
         15 . The method of  claim 1 , wherein said geometry of said physical system and said one or more extra geometries are three-dimensional. 
     
     
         16 . The method of  claim 1 , wherein said determining of said first set of geometric entity data representing one or more geometric entities on said geometry of a physical system is based on user selections received via a graphical user interface. 
     
     
         17 . The method of  claim 4 , wherein said determining of said second set of geometric entity data representing one or more geometric entities of said one or more extra geometries is based on user selections received via a graphical user interface. 
     
     
         18 . The method of  claim 1 , wherein said defining said geometry data representing said geometry of said physical system includes extracting said geometry data from data representing said first model of said physical system. 
     
     
         19 . The method of  claim 1 , wherein said defining extra geometry data representing one or more extra geometries occurs at least in part via selections of extra geometry properties received via a graphical user interface. 
     
     
         20 . The method of  claim 4 , wherein said defining extra geometry data representing one or more extra geometries occurs at least in part via selections of extra geometry properties received via a graphical user interface. 
     
     
         21 . A simulation system for adding extra geometries to a base geometry of a model of a physical system represented in terms of a combined set of differential equations, the system comprising:
 one or more physical memory devices;   one or more display devices;   one or more user input devices; and   one or more processors configured to execute instructions stored on at least one of the one or more physical memory devices, the instructions causing at least one of the one or more processors to performs steps comprising
 defining base geometry data representing a base geometry of a physical system, said base geometry data associated with a first model of said physical system, said physical system represented by a combined set of differential equations, 
 defining extra geometry data representing one or more extra geometries for a modified model based on said first model, 
 determining a first set of geometric entity data representing one or more entities of said base geometry from which to extend said one or more extra geometries, 
 adding at least a portion of said extra geometry data representing at least one of said one or more extra geometries to said determined first set of geometric entity data representing one or more entities of said base geometry by generating product data representing a product geometry for said modified model, said extra geometry data being at least a part of said product data, 
 generating equation data representing an updated combined set of differential equations for said modified model that includes said at least a portion of said product data, and 
 storing said equation data and said product data in at least one of said one or more physical memory devices. 
   
     
     
         22 . The system of  claim 21 , wherein at least a portion of said product data is stored as graphical representations configured for later display on said one or more display devices. 
     
     
         23 . The system of  claim 21 , wherein the instructions cause at least one of the one or more processors to further perform a step comprising generating a graphical representation of at least a portion of said product data, said graphical representation configured for display on at least one of said one or more display devices. 
     
     
         24 . A simulation apparatus for adding extra geometries to a model of a physical system, the apparatus comprising:
 a physical computing system comprising one or more processors, one or more user input devices, a display device, and one or more memory devices, at least one of the one or more memory devices including executable instructions for modifying a geometry of a model of a physical system represented in terms of a combined set of equations, the executable instructions causing at least one of the one or more processors to perform, upon execution, acts comprising
 in response to one or more first inputs received via said one or more user input devices, receiving a base geometry of said physical system, said base geometry associated with a model of said physical system represented in terms of a combined set of equations, 
 receiving one or more second inputs via at least one of said one or more user input devices, said second inputs defining one or more extra geometries associated with said base geometry, 
 determining one or more first geometric entities of said base geometry and one or more second geometric entities of said extra geometry, 
 adding at least one of said one or more extra geometries to said base geometry by computing a product geometry of said determined one or more first geometric entities and said one or more second geometric entities, said one or more extra geometries being at least a part of said product geometry, 
 generating an updated combined set of equations including representations of at least a portion of said product geometry, and 
 generating a graphical representation of at least a portion of said product geometry, said graphical representation configured for display on said display device. 
   
     
     
         25 . The apparatus of  claim 24 , wherein said updated combined set of equations is a combined set of non-discretized differential equations.