Void Space Domain Decomposition for Simulation Accuracy
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Solution Overview
Problem
Current domain-decomposition methods for solving partial differential equations, such as Maxwell's equations, face limitations in scaling the size of the solution vector and are plagued by boundary error issues, leading to inaccurate and inefficient simulations in the optics and RF regimes.
Innovation Solution
The Void Space Domain Decomposition (VSDD) method divides the simulation domain into subdomains, iteratively solving for residual field behavior within each subdomain while extending boundaries to minimize unrecoverable error and enhance convergence, allowing for accurate and scalable solutions to complex physical problems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional domain decomposition methods are used to divide the simulation domain into subdomains, then the computational complexity is reduced and memory requirements are decreased, but boundary errors are introduced that lead to inaccurate solutions and slow convergence
Solution Approach 1:
The simulation domain is divided into multiple non-overlapping subdomains, with each subdomain containing portions of the physical structures. This segmentation allows independent solving of each subdomain while maintaining global solution accuracy through proper boundary condition handling.
Solution Approach 2:
Void space layers are introduced as intermediary regions between subdomains containing physical structures. These void space layers act as buffers that eliminate boundary errors by ensuring that no physical structure boundaries coincide with subdomain interfaces, thereby preventing inaccurate field calculations at boundaries.
2Measurement precision
If the solution vector size is increased to improve accuracy, then the precision of the simulation results is improved, but the computational time and memory requirements increase significantly
Solution Approach 1:
By segmenting the domain into subdomains, the large global system of equations is divided into smaller local systems that can be solved independently and in parallel. This maintains solution accuracy while dramatically reducing computational time and memory requirements.
Solution Approach 2:
The method solves for fields in void space regions with higher precision than strictly necessary, which appears to be excessive computation, but this actually eliminates boundary errors and prevents the need for iterative corrections, ultimately reducing total computational time.
3Measurement precision
If more points are used in the simulation to improve accuracy, then the precision of the solution is improved, but the number of variables in the matrix equation increases making the problem harder to solve
Solution Approach 1:
The computational domain is segmented into subdomains, transforming one large complex matrix equation into multiple smaller matrix equations. Each subdomain's matrix is significantly smaller than the global matrix, making them easier to solve while maintaining overall solution precision.
Solution Approach 2:
Physical structures are extracted from the global domain and placed within specific subdomains. This allows the void space between structures to be treated separately with simplified boundary conditions, reducing the complexity of the overall system while preserving accuracy.
Data Source
AI summary
Systems and methods for computer simulation for determining a field generated from a source, with the field interacting with one or more structures. The systems and methods comprise dividing a domain into subdomains, solving iteratively for the field in a subset of the subdomains by solving for a residual field within an extended subdomain around each subdomain within the subset. If the subdomain comprises a structure, the boundary of the structure extends beyond the boundary of the extended subdomain to a second extended subdomain.