Computational Strategies in Optimizing a Real-Time Grad-Shafranov PDE Solver Using High-Level Graphical Programming and COTS Technology

Abstract

Abstract This paper describes an alternative approach based on LabVIEW that solves the critical plasma shape and position control problems in tokamaks. Input signals from magnetic probes and flux loops are the constraints for a non-linear Grad-Shafranov PDE solver to calculate the magnetic equilibrium. An architecture based on offthe-shelf multi-core hardware and graphical software is described with an emphasis on seamless deployment from development system to real-time target. A number of mathematical challenges were addressed and several generally applicable numerical and mathematical strategies were developed to achieve the timing goals. Several benchmarks illustrate what can be achieved with such an approach. commercial-off-the-shelf (COTS) multi-core computers • In the first step, compute reduced iDST instead of full iDST. • In the second step, use optimized DST leveraging sparsity. Hardware and Software Grad-Shafranov PDE • Ψ is the poloidal flux function; • j is the current density; • R is the radial component; • Z is the axial component. • 33x65 grid Benchmarks Benchmarks for the real-time Grad-Shafranov solver and simultaneous function paramerisation and Grad-Shafranov solvers using 8 cores

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