From Kernels to Solvers: Performance-Portable High-Order PDE Simulation in Nektar++

Nektar++ is an open-source spectral/hp element framework for the numerical solution of partial differential equations (PDEs), widely used for high-order simulations in computational fluid dynamics (CFD) and related fields. To fully exploit the capabilities of modern heterogeneous high-performance computing (HPC) systems, including graphical processing unit (GPU)-accelerated platforms, the framework is undergoing a major redesign aimed at performance portability and long-term maintainability. The new code enables efficient execution on NVIDIA, AMD, and Intel GPUs, while retaining high-performance CPU implementations single instruction, multiple data (SIMD) vectorisation. This is achieved via a unified backend architecture supporting CUDA, HIP, SYCL, and SIMD operations, enabling device-independent implementation of high-level solver logic while allowing hardware-specific optimisation of performance-critical building blocks such as elemental operators. Building on results previously presented for elemental kernels, this work reports recent progress on optimised global operators, including linear system solvers, evaluated using industry-standard Center for Efficient Exascale Discretizations (CEED) Bake-off Problems (BPs). We additionally demonstrate emerging multi-GPU capabilities and apply the operator-based design to the solver level by refactoring the unsteady advection and compressible Euler solvers around a unified operator interface within the redesigned framework. The resulting solver architecture cleanly separates numerical formulation from execution backends, enabling a single code path to target serial, vectorised, and GPU platforms. These developments represent an important step towards enabling scalable, portable, and production-ready high-order simulations on current and future heterogeneous HPC systems.