Systolic Array for Solving Partial Differential Equations

The patent divides the computational domain into multiple discrete nodes and organizes them into a mesh structure. Each node represents an independent computational unit that can be processed separately. This segmentation enables parallel processing across multiple nodes simultaneously, dramatically reducing the overall computational time required to solve differential equations while maintaining the accuracy of the solution.

The patent transitions from sequential one-dimensional processing to multi-dimensional parallel processing by organizing computational nodes in a spatial mesh structure. The systolic array architecture processes nodes across multiple dimensions (spatial and temporal) simultaneously, allowing the system to evaluate multiple points in the domain at once rather than sequentially, thus achieving exponential speedup.

The systolic array architecture is designed with a universal structure that can solve multiple types of differential equations (parabolic, hyperbolic, elliptic) by configuring the same hardware with different parameters and boundary conditions. The mesh-based node organization and standardized computation pipeline allow the system to adapt to various problem types without requiring dedicated hardware for each equation type, thus maintaining versatility while achieving high computational efficiency.

The patent achieves versatility through parameter configuration rather than structural changes. The same systolic array hardware can solve different differential equations by adjusting parameters such as the discretization scheme, boundary condition values, and equation coefficients. This parameter-based adaptability allows a single efficient hardware architecture to handle a wide range of differential equation types.

The patent segments the computational domain into a mesh of discrete nodes, where each node is an independent processing unit in the systolic array. This segmentation allows the system to handle large domains by distributing computations across many nodes in parallel. The modular nature of the mesh structure means that increasing domain size simply adds more nodes to the array rather than increasing the complexity of individual computational units, enabling scalable solutions for large domains.

The patent resolves the complexity issue by transitioning to a multi-dimensional parallel architecture. Instead of increasing sequential processing power to handle larger domains, the system uses a two-dimensional mesh structure processed by a systolic array, where both spatial dimensions and time steps are handled in parallel. This dimensional transformation converts what would be a computationally intensive sequential problem into a efficiently parallelizable problem.

The patent merges multiple computational operations into a unified systolic array architecture. Instead of using separate processing units for different aspects of the differential equation solution (advection, diffusion, boundary conditions), the system combines all these functions into a single integrated mesh-based parallel processor. This merging reduces the overall system complexity by eliminating the need for complex interconnections between multiple specialized units while achieving high parallel processing speed.

The systolic array architecture is designed to be self-organizing and self-synchronizing. Each node in the mesh automatically receives data from its neighbors and performs computations in a coordinated fashion without requiring complex external control logic. The data flows naturally through the array in a wave-like pattern, with each node serving itself by computing based on locally available information from adjacent nodes, thereby reducing the need for complex control systems.