Simulation System for Coupled Systems on Spatial Dimensions
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current computer design systems lack the capability to effectively model and simulate complex physical systems that require additional geometries beyond the standard spatial dimensions, limiting their ability to handle complex environments and coupled physical phenomena.
Innovation Solution
A simulation method and system that allow for the definition and addition of extra geometries to a base model, represented by combined sets of equations, enabling the creation of product geometries through Cartesian products and facilitating the solution of coupled systems of partial differential equations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If computer design systems use standard spatial dimensions only, then the system complexity remains manageable, but the capability to model complex physical systems with additional dimensions is limited
Solution Approach 1:
The patent extends the modeling capability from standard 3D spatial dimensions to higher dimensions by introducing extra geometric entities (4D, 5D, etc.). This allows the system to model complex physical systems such as spacetime events, multi-phase flows, and coupled phenomena that require additional dimensional parameters, thereby resolving the contradiction between modeling capability and system complexity.
Solution Approach 2:
The patent segments the geometric model into base geometry (standard spatial dimensions) and extra geometry (additional dimensions). This segmentation allows the system to handle complex models by treating different dimensional aspects as separate but coupled entities, making the overall system more manageable while enhancing modeling versatility.
2Adaptability or versatility
If extra geometries are added to extend the model dimensions, then the modeling capability for complex environments is enhanced, but the computational complexity and equation system complexity increase
Solution Approach 1:
The patent implements a nested structure where extra geometric entities are embedded within the base geometry framework. The product geometry is formed by nesting extra geometry dimensions onto the base spatial dimensions, allowing the system to handle enhanced modeling capability while organizing the computational complexity in a hierarchical, manageable structure.
Solution Approach 2:
The patent creates a universal modeling framework that can handle both standard 3D geometries and higher-dimensional geometries using the same base infrastructure. The combined set of equations and unified geometric entity management system provides multi-functionality, allowing the system to model various complex physical phenomena without requiring separate computational frameworks for each dimension type.
3Adaptability or versatility
If the geometric representation is extended to include extra dimensions, then the ability to represent coupled physical phenomena is improved, but the data structure complexity and processing requirements increase
Solution Approach 1:
The patent merges the base geometry data structures with extra geometry data structures to form a unified product geometry representation. The geometric entity data, material properties, and equation systems are combined into an integrated structure that efficiently represents coupled physical phenomena across multiple dimensions while avoiding the need for separate data structures for each dimension type.
Solution Approach 2:
The patent introduces product geometry entities as intermediaries that bridge the base geometry and extra geometry. These product entities serve as mediators that connect the standard spatial dimensions with the additional dimensions, allowing the system to represent coupled phenomena while managing data structure complexity through a standardized interface layer.
Data Source
AI summary
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.