Hybrid Mesh-Point Cloud Discretization for Deformation Simulation
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Solution Overview
Problem
Existing physics simulation methods struggle with complex geometries and significant deformations, leading to inefficiencies and instability due to excessive mesh deformation and high computational costs, particularly in simulations involving inverse problems and optimal control.
Innovation Solution
A hybrid discretization method that combines meshing and meshless approaches by discretizing objects with meshes and point clouds, allowing for efficient modeling of deformations through iterative simulation runs and updating of point cloud positions, thereby avoiding mesh degeneration and maintaining geometric accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If mesh-based simulation methods are used for complex geometries, then geometric accuracy is improved, but mesh deformation becomes excessive leading to instability
Solution Approach 1:
The simulation domain is segmented into two distinct discretization representations: mesh-based regions for objects requiring high geometric accuracy and point cloud-based regions for objects subject to large deformations. This segmentation allows each region to be treated with the most appropriate method, preventing mesh degeneration while maintaining geometric fidelity where needed.
Solution Approach 2:
Different discretization qualities are applied locally to different objects or regions within the same simulation. Mesh-based discretization with high geometric precision is applied to rigid or slowly deforming objects, while point cloud-based discretization is applied to objects undergoing significant deformation. This local differentiation resolves the contradiction by optimizing each region's representation according to its specific requirements.
2Manufacturing precision
If mesh-based methods are used to maintain geometric accuracy, then manufacturing precision is improved, but computing resources become expensive
Solution Approach 1:
The computational domain is divided into mesh-based and point cloud-based regions, allowing expensive mesh-based calculations to be confined only to areas where high geometric accuracy is essential, while point cloud methods handle the rest at lower computational cost.
Solution Approach 2:
High computational resources are allocated locally to regions requiring geometric accuracy through mesh-based discretization, while point cloud-based discretization provides a computationally efficient alternative in regions where geometric precision is less critical or where large deformations occur.
3Productivity
If isogeometric analysis methods are used, then computational efficiency is improved, but complex geometries cannot be described
Solution Approach 1:
The hybrid discretization framework creates a universal simulation approach that can handle both simple and complex geometries while maintaining computational efficiency. By supporting both mesh-based and point cloud-based discretizations within the same framework, the method achieves multi-functionality, adapting to different geometry types and deformation characteristics as needed.
Data Source
AI summary
The disclosure relates to a computer-implemented method for performing a deformation-based physics simulation described by a partial differential equation. The method comprises providing a geometrical model representing a portion of the real world. The method comprises performing a hybrid discretization of the model. The performing of the hybrid discretization comprises discretizing one or more first objects in the portion each with a mesh and one or more second objects in the portion each with a point cloud. The method comprises one or more iterations. Each iteration comprises performing a simulation run based on a discretization of the partial differential equation and on the hybrid discretization. The iteration comprises assessing a deformation as a result of the simulation run. The deformation corresponds to a shape deformation of the one or more second objects. The iteration comprises updating the hybrid discretization to model the deformation by moving points of a point cloud.