Simulation systems with mapping between non-conformal geometries
Coupling of physics solutions (e.g., a first physics solution and a second physics solution) in a multi-physics simulation that includes non-conformal spaces can use extrapolation to determine data values for unmapped nodes by computing extrapolated values based on both mapped values from mapped nodes and data for unmapped nodes. The extrapolated values for an unmapped node are computed using a set of equations that include mapped values from nearby mapped nodes and data for nearby unmapped nodes. The methods and systems can provide improved computational efficiency by reducing the amount of memory required for the computations.
1 . A non-transitory machine readable medium storing executable program instructions which when executed by a data processing system cause the data processing system to perform a method for multi-physics simulation, comprising:
simulating characteristics of a first physics for a physical object represented by a first mesh model in a source space, characteristics of the first physics associated with data values at nodes in the source space;
receiving a second mesh model representing the physical object in a target space having nodes, the second mesh model for a second physics of the physical object;
determining a mapping of the data values from the nodes in the source space to the nodes in the target space, at least some of the nodes in the target space being mapped nodes, each mapped node to receive, through the mapping, at least some data values from the nodes in the source space,
identifying a set of one or more nodes in the target space as unmapped nodes, each unmapped node without receiving any data values from the nodes in the source space;
determining, for each unmapped node in the target space, a set of nearby neighbor nodes in the target space including two or more mapped nodes and two or more unmapped nodes;
creating an extrapolation relationship between the two or more mapped nodes and the two or more unmapped nodes in the set of nearby neighbor nodes for the unmapped node in the target space;
generating data values for the unmapped node in the target space based on the relationship using data values of the two or more mapped nodes of the set of nearby neighbor nodes and positions of the two or more unmapped nodes in the set of nearby neighbor nodes; and
simulating characteristics of the second physics for the physical object represented by the second mesh model in the target space based on the data values associated with the first physics received from the source space, the characteristics of the first physics and the characteristics of the second physics simulated for a design of the physical object before the physical object is manufactured.
2 . The non-transitory machine readable medium as in claim 1 , wherein the set of unmapped nodes are in a portion of the target space that does not overlap with the source space and the two or more mapped nodes are in a portion of the target space that does overlap with the source space, and wherein the data values at nodes in the source space represent one or more physical values from a first physics solution about a simulated object being designed in a simulation system in the data processing system.
3 . The non-transitory machine readable medium as in claim 2 , wherein the nodes in the source space are nodes in a first mesh, and the nodes in the target space are nodes in a second mesh, and the first mesh and the second mesh have non-conformal geometries.
4 . The non-transitory machine readable medium as in claim 2 , wherein the source space and the target space are one of: (a) a surface, or (b) a volume.
5 . The non-transitory machine readable medium as in claim 3 , wherein the one or more physical values from the first physics solution are used to compute one or more physical values in a second physics solution to determine the characteristics of the second physics for the simulated object before the physical object is manufactured based on the simulated object, and wherein the mapping couples the first physics solution to the second physics solution.
6 . The non-transitory machine readable medium as in claim 5 , wherein the data values at each of the two or more unmapped nodes are extrapolated from the data values from the two or more mapped nodes and coefficient data of the two or more unmapped nodes in the set of nearby neighbor nodes.
7 . The non-transitory machine readable medium as in claim 5 , wherein a neighbor node in the set of nearby neighbor nodes is nearby to an unmapped node when: (a) the neighbor node is within a first radius from the unmapped node; or (b) the neighbor node is in a face that shares an edge with a face containing the unmapped node; or (c) the face containing the unmapped node shares a node with a face containing the neighbor node.
8 . The non-transitory machine readable medium as in claim 6 , wherein the relationship comprises a set of equations that include first physics solution data from nearby mapped nodes and coefficients for nearby unmapped nodes.
9 . The non-transitory machine readable medium as in claim 8 , wherein, for each unmapped node, computed contributions from all nearby neighbor nodes are combined in a weighted average.
10 . The non-transitory machine readable medium as in claim 8 , wherein a number of unmapped nodes in the set of equations is equal to a number of equations in the set of equations.
11 . A method performed by a data processing system for multi-physics simulation, the method comprising:
simulating characteristics of a first physics for a physical object represented by a first mesh model in a source space, characteristics of the first physics associated with data values at nodes in the source space;
receiving a second mesh model representing the physical object in a target space having nodes, the second mesh model for a second physics of the physical object;
determining a mapping of the data values from the nodes in the source space to the nodes in the target space, at least some of the nodes in the target space being mapped nodes, each mapped node to receive, through the mapping, at least some data values from the nodes in the source space,
identifying a set of one or more nodes in the target space as unmapped nodes, each unmapped node without receiving any data values from the nodes in the source space;
determining, for each unmapped node in the target space, a set of nearby neighbor nodes in the target space including two or more mapped nodes and two or more unmapped nodes;
creating an extrapolation relationship between the two or more mapped nodes and the two or more unmapped nodes in the set of nearby neighbor nodes for the unmapped node in the target space;
generating data values for the unmapped node in the target space based on the relationship using data values of the two or more mapped nodes of the set of nearby neighbor nodes and positions of the two or more unmapped nodes in the set of nearby neighbor nodes; and
simulating characteristics of the second physics for the physical object represented by the second mesh model in the target space based on the data values associated with the first physics received from the source space, the characteristics of the first physics and the characteristics of the second physics simulated for a design of the physical object before the physical object is manufactured.
12 . The method as in claim 11 , wherein the set of unmapped nodes are in a portion of the target space that does not overlap with the source space and the two or more mapped nodes are in a portion of the target space that does overlap with the source space, and wherein the data values at nodes in the source space represent one or more physical values from a first physics solution about a simulated object being designed in a simulation system in the data processing system.
13 . The method as in claim 12 , wherein the nodes in the source space are nodes in a first mesh, and the nodes in the target space are nodes in a second mesh, and the first mesh and the second mesh have non-conformal geometries.
14 . The method as in claim 12 , wherein the source space and the target space are one of: (a) a surface, or (b) a volume.
15 . The method as in claim 13 , wherein the one or more physical values from the first physics solution are used to compute one or more physical values in a second physics solution to determine the characteristics of the second physics for the simulated object before the physical object is manufactured based on the simulated object, and wherein the mapping couples the first physics solution to the second physics solution.
16 . The method as in claim 15 , wherein the data values at each of the two or more unmapped nodes are extrapolated from the data values from the two or more mapped nodes and coefficient data of the two or more unmapped nodes in the set of nearby neighbor nodes.
17 . The method as in claim 15 , wherein a neighbor node in the set of nearby neighbor nodes is nearby to an unmapped node when: (a) the neighbor node is within a first radius from the unmapped node; or (b) the neighbor node is in a face that shares an edge with a face containing the unmapped node; or (c) the face containing the unmapped node shares a node with a face containing the neighbor node.
18 . The method as in claim 16 , wherein the relationship comprises a set of equations that include first physics solution data from nearby mapped nodes and coefficients for nearby unmapped nodes.
19 . The method as in claim 18 , wherein, for each unmapped node, computed contributions from all nearby neighbor nodes are combined in a weighted average.
20 . The method as in claim 18 , wherein a number of unmapped nodes in the set of equations is equal to a number of equations in the set of equations.