Spline-based electromagnetic simulation on HPC platforms

Accurate simulations of multiscale electromagnetics problems have far-reaching implications for numerous scientific disciplines. The same physics governs problems of importance for DOE such as motor/generator design optimization for improved energy efficiency and ion trap design for quantum computing. Simulations are currently suboptimal in the sense that they either lack the required fidelity or simply cannot be executed within users’ resource constraints. Such simulation problems involve complex materials, multiscale meshing challenges, and geometries that may yield >100M degrees of freedom. The workflow of computational electromagnetics has not changed in 40 years. All users recognize that two of the most frustrating steps in this workflow are meshing and runtime execution. This program will extend an already-commercialized electromagnetics software package with distributed solution capability and spline-based simulation technology in order to eliminate user meshing and achieve massive increases in simulation performance. The current software supports multi-core and multi-GPU capability and an in- development version incorporates a ASCR-funded exascale linear algebra software suite to address extremely large- scale electromagnetics design and analysis problems. By incorporating spline-based simulation, meshing is eliminated and results in a geometry-perfect representation for numerical solution. Extremely high-order accuracy is achieved by using the same spline basis used to create the geometry. This provides the user with tight integration with the underlying geometry and potential for automatic refinement. All the while, this numerical approach will be integrated with exascale linear algebra to address problems of the largest scale. This work has two major objectives. First, the team will demonstrate the feasibility and performance benefits of adopting U-spline geometry representation and numerical solutions. The computer aided design software will tightly integrate with the underlying numerical solver. The new simulation approach will retain all of the benefits of the existing commercial software including multi-GPU capability and low-rank matrix compression. The software will be demonstrated to provide high order accuracy on complex problems such as large-scale ion traps. Second, the team will demonstrate an initial capability for the spline-based low-rank compressed matrix solution integrated with a exascale linear algebra solver extended for low-rank matrices. Performance scaling will be shown using several real-world examples relevant to the small business’s other technical focuses. By achieving this objective, the team will have the baseline capability available for extension and performance optimization in Phase II. This new software will provide an important leap in computational capability for all users requiring electromagnetic design and analysis capability. We anticipate these improvements to be particularly useful within the quantum computing and materials fields as well as fundamental metrology. These new capabilities will also enable the academia, government, and small business to provide high performance results using a simulation-as-a-service business model since not all users may have access to large-scale computational resources.