Solver Hardware Dispatch for Parallel Differential Equation Solving
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Solution Overview
Problem
Current computer systems face inefficiencies in solving large and complex differential equations due to sequential processing, data transfer bottlenecks in parallel computing, and limitations imposed by Amdahl's law, leading to slow simulation times and high computational costs, especially for problems requiring strong vertical scaling.
Innovation Solution
A specialized computing architecture comprising an interface computer, dispatch computer, and solver units, including Differential Equation Accelerators (DEAs), optimized for parallel processing and efficient distribution of problem packages to solvers based on availability and priority, with concurrent subdomain solving and synchronized data sharing among DEAs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If sequential processing is used to solve differential equations, then computational accuracy is maintained, but simulation time increases significantly
Solution Approach 1:
The computing domain is segmented into multiple subdomains that can be processed in parallel by different solver units. Each subdomain is independently solved while maintaining boundary conditions, enabling concurrent computation that reduces total simulation time without sacrificing overall accuracy.
Solution Approach 2:
The patent transitions from sequential time-based processing to parallel spatial processing by introducing multiple solver units that operate simultaneously on different subdomains. This dimensional shift from single-threaded to multi-threaded execution fundamentally changes how computation progresses, reducing simulation time while maintaining accuracy through synchronized updates.
2Productivity
If parallel computing is used to reduce simulation time, then computational speed improves, but data transfer bottlenecks increase
Solution Approach 1:
The patent extracts and minimizes data transfer requirements by designing solver units with local computation capabilities that reduce dependency on inter-unit data exchange. Each solver unit processes subdomains with minimal boundary condition exchanges, extracting the essential computational work from data transfer operations.
Solution Approach 2:
A dispatch computer acts as an intermediary between problem packages and solver units, managing task distribution and coordination. This intermediary layer abstracts the complexity of direct data transfer between solver units, optimizing the communication overhead and enabling efficient parallel processing.
3Productivity
If dedicated solver hardware is implemented, then computational efficiency improves, but device complexity increases
Solution Approach 1:
The dispatch computer serves multiple functions: it manages the queue of problem packages, selects appropriate solver units based on availability and problem characteristics, distributes subdomains, and coordinates synchronization. This multi-functional design reduces overall system complexity by consolidating control logic in a single component rather than requiring complex interconnections between all solver units.
Solution Approach 2:
Solver units operate as self-contained modules that autonomously process assigned subdomains without requiring constant external intervention. Each unit independently manages its computation, handles boundary conditions, and synchronizes with others, reducing the complexity of centralized control while maintaining high computational efficiency.
4Productivity
If solver units are assigned based on availability and priority, then resource utilization maximizes, but scheduling complexity increases
Solution Approach 1:
The patent implements dynamic solver selection where the dispatch computer continuously monitors solver availability and adjusts assignments in real-time. This dynamic approach allows the system to adapt to changing computational loads and solver states, maximizing utilization without requiring complex predetermined scheduling algorithms.
Solution Approach 2:
The dispatch computer receives feedback about solver availability and problem completion status, using this information to make intelligent assignment decisions. This feedback mechanism enables simple yet effective scheduling that maximizes resource utilization by assigning problems to available solvers based on current system state rather than complex predictive algorithms.
Data Source
AI summary
Embodiments relate to a computing system for solving differential equations. The system is configured to receive problem packages corresponding to problems to be solved, each comprising at least a differential equation and a domain, and to select a solver of a plurality of solvers, based upon availability of each of the plurality of solvers. A dispatch computer selects a solver by monitoring the plurality of solvers, and responsive to a solver becoming available, determines if a received problem package having at least a threshold priority level can be solved by the solver. Otherwise, the dispatch computer generates a plurality of solver scenarios each reflecting a permutation of received problem packages assigned to solvers estimated to become available within a threshold period of time, and assigns the problem packages in accordance with a solver scenario having a highest utilization score.