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    This study introduces a hardware-based parallel algorithm for real-time haptic simulations. The Field-Programmable Gate Array (FPGA) implementation accelerates finite-element (FE) analysis of deformable objects.

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    Area of Science:

    • Computational Physics
    • Robotics
    • Computer Engineering

    Background:

    • Real-time simulation of haptic interactions with deformable objects requires high computational power.
    • Finite-element (FE) analysis demands solving large equation systems at 100-1,000 Hz for stability and fidelity.

    Purpose of the Study:

    • To propose a hardware-based parallel implementation of the Preconditioned Conjugate Gradient (PCG) algorithm for FE-based deformation models.
    • To achieve real-time simulation rates for complex haptic interactions.

    Main Methods:

    • Developed a parallel PCG algorithm utilizing numerous fixed-point computing units on a Field-Programmable Gate Array (FPGA).
    • Minimized quantization and overflow errors using dynamic scaling and preconditioning.
    • Detailed analysis of numerical accuracy, architecture design, parallelism, and scalability.

    Main Results:

    • The FPGA implementation achieved real-time simulation of 3D linear elastic deformation models.
    • Simulations with 1,500 nodes reached update rates up to 2,500 Hz.
    • Demonstrated high computational speed for solving linear systems in FE analysis.

    Conclusions:

    • Hardware-based parallel PCG on FPGAs significantly accelerates real-time haptic simulations.
    • The proposed method enhances simulation fidelity and stability for deformable objects.
    • This approach is scalable and accurate for complex FE-based deformation models.