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ABSTRACT: The proposed project will remove the computational bottleneck in the currently adopted numerical treatment of exterior 3D magnetic fields around high-current pulsed power devices. Existing simulators introduce computationally expensive and nonphysical magnetic diffusion in the exterior region. In contrast, our approach is physically and mathematically rigorous and dramatically improves both accuracy and speed of the computation. In Phase I, our innovative methods for both quasi-static and wave components of 3D magnetic fields were developed, tested and validated on numerical and analytical model problems, both linear and nonlinear. Specific and verifiable advantages of our methodology include: (i) high accuracy due to rigorous analytical treatment of the exterior fields; (ii) no need for dense system matrices; (iii) no singular integration kernels; (iv) single scalar (as opposed to vector) potentials; (v) negligible computational overhead for the plasma simulator; (vi) ease of coupling with legacy interior codes such as Mach3; (vii) parallelizability; (viii) applicability to time-varying geometries. In Phase II, our algorithms will be implemented as robust software tools, combined with the interior MHD codes Mach3 and WARPX, and validated on the appropriate Air Force problems. Coupled field-circuit co-simulation capabilities for complex devices will be included. BENEFIT: Air Force missions require improvements and innovations in the modeling of 3D magnetic fields. The proposed project will provide innovative methods and software for highly efficient and precise computation of magnetic fields and waves around high-current pulsed power application systems. Potential dual and commercial applications are vast and diverse: fields around plasma fusion devices, magnetic recording, electromagnetic devices for oil exploration, quasi-static and electrodynamics problems of plasmonics (one of the most vibrant areas of nano-photonics), electromagnetic interference and capacitance of interconnects in microelectronics. The new modeling and simulation tools for 3D electromagnetic fields will help Air Force to: (i) assess technologies, devices, and materials for new high-current pulsed power application systems; (ii) better evaluate the performance at the early design stages; (iii) set requirements for testing; reduce the cost and time of testing. The modeling and design tools will provide reduction in cost and time-to-market through reduced experimental R&D, design cycle, and streamlined laboratory testing.