A highly efficient matrix-free Helmholtz operator with single-instruction multipledata (SIMD) vectorisation is implemented in Nektar++  and applied to the simulation of anisotropic heat transport in tokamak edge plasma. A tokamak is currently the leading candidate for a practical fusion reactor using the magnetic confinement approach to produce electricity through controlled thermonuclear fusion. Predicting the transport of heat in magnetized plasma is important to designing a safe tokamak design. Due to the ionized nature of plasma, the heat conduction of the magnetized plasma is highly anisotropic along the magnetic field lines. In this study, a variational form is proposed to simulate the anisotropic heat transport in magnetized plasma and the details of its mathematical derivation and implementation are presented. To accurately approximate the thermal load of plasma deposition on the wall of tokamak chamber, highly scalable and efficient algorithms are crucial. To achieve this, a matrix-free Helmholtz operator is implemented in the Nektar++ framework, utilising sum-factorisation to reduce the operation count and increase arithmetic intensity, and leveraging SIMD vectorisation to accelerate the computation on modern hardware. The performance of the implementation is assessed by measuring throughput and speed-up of the operators using deformed and regular quadrilateral and triangular elements.
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