Sector Meshing for Object Interaction Simulation
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Solution Overview
Problem
Complex computer simulations of object interactions require extensive computations, leading to long run times, as they typically involve numerous particles, many of which are not actively engaged or significantly influential, necessitating a reduction in computational effort without compromising accuracy.
Innovation Solution
The method involves generating particles from geometric data, grouping them into sectors, and identifying only active and neighboring particles within a limited region of influence, focusing computations on relevant particles at each time step, thereby reducing the number of computations needed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all particles in the system are considered in computations at each time step, then accuracy of simulation results is maintained, but simulation run time becomes excessively long
Solution Approach 1:
The system divides all particles into two distinct groups: active particles that are currently engaged in the engagement and have significant influence on the outcome, and inactive particles that are not currently involved. This segmentation allows computations to be performed only on active particles and their neighboring particles, rather than all particles in the system, thereby reducing computational complexity and run time while maintaining accuracy for the engaged region
Solution Approach 2:
The patent applies different computational treatment to different regions of the particle system. Active particles and their neighbors receive full computational attention with detailed physics calculations, while inactive particles are excluded from computations. This local quality approach ensures high accuracy where it matters (in the engagement zone) while reducing overall computational burden
2Reliability
If computations are performed on all particles in the system, then comprehensive physical phenomena are captured, but computational complexity increases significantly
Solution Approach 1:
The patent extracts and isolates only the subset of particles that are relevant to the current engagement state - specifically active particles and their neighboring particles within a defined region of influence. By taking out this specific subset from the complete particle system, the method reduces computational complexity from O(N) where N is the total number of particles to O(n) where n is the much smaller number of active and neighboring particles, while still capturing the essential physics of the engagement
3Productivity
If the number of particles in the computational mesh is reduced, then simulation run time decreases, but fidelity of results may be compromised
Solution Approach 1:
The patent implements a dynamic particle selection process where the set of active particles and their neighbors is recalculated at each time step based on the current engagement state. This dynamic approach ensures that as the engagement evolves, the computational mesh automatically adjusts to include the relevant particles at each moment, maintaining fidelity throughout the simulation while optimizing run time through selective computation
Data Source
AI summary
Methods for computer-implemented simulation for the interaction of two or more objects are provided. Data describing particles that represent each of the objects is generated from geometric data for objects. The data for each particle describes a mass density, velocity and energy at a position of the corresponding object. The particles are grouped into sectors to define a computational mesh comprising a plurality of sectors, wherein each sector is a volume region at a position in space in which particles associated with the objects may reside. For each of a plurality of select particles, so called neighboring particles are determined that are within a region of influence with respect to a select particle. Computations are performed based on laws of conservation of mass, energy and momentum to produce updated values for mass, velocity, energy, pressure, stress and position for the particles at each of a plurality of time steps. According to one aspect, when determining neighboring particles for a given select particle, a search is made through a limited or bounded volume region with respect to the select particle that consists of the region of influence for the select particle at the previous time step and within those sectors in contact with or bordering the region of influence at the previous time step. According to another aspect, the plurality of select particles are identified as those particles that reside in an active sector, wherein an active sector is a sector that contains, or is adjacent to a sector that contains, particles that is actively involved in the engagement between the two objects. For example, an active sector is a sector that contains, or is adjacent to a sector that contains, at least one particle that has a velocity, pressure or stress greater than a corresponding predetermined amount.