In high intensity hadron beam accelerators, specifically those supported through the DOE High Energy Physics program, the space-charge effect from the interactions between charged particles can have significant impact on beam dynamics, including particle loss along the accelerator. At the beam pipe, these effects and losses can be especially pronounced. As the facilities for high energy physics grow in size, cost (in building, maintenance, and simulation energy usage), and as the constraints on beam loss increase, it is becoming more important to be able to accurately predictthe space-charge effect on beam loss. Advanced numerical and computational approaches are needed to build predictive models prior to simulations. Through a DOE Phase I project called MACH-B (Multipole Accelerator Codes for Hadron Beams), a highly-scalable, parallel, HPC Fast Multipole Method (FMM)-based tool will be developed for higher fidelity modeling of particle accelerators for high energy physics. MACH-B tools will be engineered within the next generation of the DOE-funded Fermilab Synergia software system on heterogeneous architectures, which will rely further on the DOE-funded Kokkos infrastructure to provide source level portability of the code base between Central Processing Unit (CPU) and Graphics Processing Unit (GPUs) hardware. MACH-B tools will be parallelized for peak performance and minimal communication overhead and provide higher fidelity and resolution for the accelerator community than is currently available, saving computational resources, energy, time and money. In MACH-B, a software module for the Synergia code base will be involve (1) a Fast Multipole Method (FMM) tool, (2) a Boundary Integral Solver (BIS), (3) an Embedded Boundary Solver (EBS), and (4) state-of-the-art parallelization methods using Kokkos as an ion layer. The FMM will be designed as kernel-independent to allow for maximum flexibility for multiple PDEs and has been shown to scale well to hundreds of thousands of processors by Reservoir researchers. The BIS will be designed using Quadratures by Expansion, which has been designed for 3D problems, works with unstructured geometries, can perform on-the-fly quadratures works for most kernels, including singular and hypersingular ones, and can be hierarchically parallelized. The results will be a tool that offers great flexibility and options for high-energy computational physicists. Across the government applied research and development programs, we anticipate new applications such as plasma physics simulations, radar and optics simulations, and varied other scientific-computing heavy fields such as electromagnets, fluid mechanics, and electrostatics. For industry, applications include more efficient oil and gas exploration, better automotive and aerospace design and greater efficiency and accuracy in commercial manufacturing.
