The plane wave transform (PWT) is a critical operation in computational electromagnetics. Accurate multilevel implementations of the PWT often rely on FFT-based interpolation and filtering operations when performing inter-level pattern aggregation and disaggregation. This presentation reports an alternative, explicitly sparse representation of the PWT. For a 2-D implementation, it is shown that the complexity of the resulting multilevel PWT is $O({N} \text{log}{N})$.

A mixed-order divergence-conforming method for pyramidal cells is presented for use with a locally corrected Nyström discretization of a volume integral equation. The function space is developed from a mixed-order divergence-conforming interpolatory basis set. Determination of a suitable pyramidal quadrature rule is discussed. Results are presented for a volume integral equation discretization of the electric-field integral equation and applied to plane wave scattering from a dielectric sphere.

A locally corrected Nystrom method is presented that better models a mixed-order, divergence-conforming space on triangular cells. The theory is developed for a space that is complete to the same order for both the unknown quantity and its divergence. The method is implemented for the electric field integral equation, and convergence results are presented for scattering from a perfectly conducting sphere.

Plasmonic modes offer the potential to achieve PetaVolts per meter fields, that would transform the current paradigm in collider development in addition to non-collider searches in fundamental physics. PetaVolts per meter plasmonics relies on collective oscillations of the free electron Fermi gas inherent in the conduction band of materials that have a suitable combination of constituent atoms and ionic lattice structure. As the conduction band free electron density, at equilibrium, can be as high as $\rm 10^{24}cm^{-3}$, electromagnetic fields of the order of $\rm 0.1 \sqrt{\rm n_0(10^{24}cm^{-3})} ~ PVm^{-1}$ can be sustained by plasmonic modes. Engineered materials not only allow highly tunable material properties but quite critically make it possible to overcome disruptive instabilities that dominate the interactions in bulk media. Due to rapid shielding by the free electron Fermi gas, dielectric effects are strongly suppressed. Because the ionic lattice, the corresponding electronic energy bands and the free electron gas are governed by quantum mechanical effects, comparisons with plasmas are merely notional. Based on this framework, it is critical to address various challenges that underlie PetaVolts per meter plasmonics including stable excitation of plasmonic modes while accounting for their effects on the ionic lattice and the electronic energy band structure over femtosecond timescales. We summarize the ongoing theoretical and experimental efforts as well as map out strategies for the future. Extreme plasmonic fields can shape the future by not only bringing tens of TeV to multi-PeV center-of-mass-energies within reach but also by opening novel pathways in non-collider HEP. In view of this promise, we invite the scientific community to help realize the immense potential of PV/m plasmonics and call for significant expansion of the US and international R\&D program.

This is the Snowmass2021 Energy Frontier (EF) Beyond the Standard Model (BSM) report. It combines the EF topical group reports of EF08 (Model-specific explorations), EF09 (More general explorations), and EF10 (Dark Matter at Colliders). The report includes a general introduction to BSM motivations and the comparative prospects for proposed future experiments for a broad range of potential BSM models and signatures, including compositeness, SUSY, leptoquarks, more general new bosons and fermions, long-lived particles, dark matter, charged-lepton flavor violation, and anomaly detection.

In this paper, a boundary integral equation method is presented for the prediction of electrostatic fields in regions comprising piecewise-homogeneous electrolytes. The integral equation is discretized using the Locally Corrected Nystrom method. The method is validated through comparison of computed results to the analytic solution for a rectangular box filled with a piecewise-homogeneous electrolyte.

In this paper, a technique to convert a locally corrected Nystrom discretization into a moment method discretization is detailed. The method is general and does not rely directly on any specific relationship between the basis functions used to compute the local corrections and the basis and test functions used in the moment method. The technique is applied to a quasi-magnetostatic volume integral equation for both interpolatory and algebraically constrained moment method bases. Numerical results for a variety of problems in terms of error convergence, system condition number, and degrees-of-freedom are provided.

The cooperative anisotropic hysteresis model of ferromagnetic susceptibility has been recast in exponential form. After field reversals, susceptibility increases cooperatively with magnetization change and then decreases toward saturation until it becomes reversible again. The proposed exponential decrease in susceptibility agrees with measurements and with the Jiles-Atherton Langevin anhysteretic model; our model also accurately represents virgin, minor and first order reversals to saturation. The model is validated experimentally using a thin steel ring and pipe and a thin disk in a vibrating sample magnetometer, all isolated from stress and thermal effects by applying half cycles of sinusoidal magnetic field or using quasistatic field steps to remove eddy currents and stabilize viscosity. Precisely calibrated field and magnetization changes M(H) are controlled and measured with a National Instrument data acquisition system and custom LabView software, and differential susceptibilities X (M) are computed. The proposed model is a function of measurable physical constants including initial susceptibility, X-i, anhysteretic field, H-anh, saturation magnetization, M-s, and normalized symmetric crystalline and domain coupling anisotropy functions, X-r and X-c.

A broad-band Augmented-Muller (A-Muller) surface integral equation method for scattering from material objects is presented. The formulation incorporates surface electric and magnetic charges into the conventional Muller formulation with added constraints on the normal magnetic and electric fields. A new technique to extract the static fields is introduced which improves accuracy of computing scattered near fields at very low frequencies. The (A-Muller) formulation is discretized using the locally corrected Nystrom (LCN) method. Numerical results show that the method is high-order accurate and stable over a broad frequency range from arbitrarily low to high frequencies for simply connected, multiply connected, highly lossy, high contrast and complex material geometries. The proposed formulation does not incorporate line charges, charge continuity constraints, or any frequency scaling of the degrees of freedom

Whistler mode waves are a type of electromagnetic plasma wave and play a dominant role in the energy dynamics of the near-earth space environment and associated space weather processes. Ground-based observations of these waves are important for numerical model validation, space weather monitoring, and discovery science. Unfortunately, ground-based observations are often challenging to interpret since information about traversal through the ionosphere and distance propagated in the earth-ionosphere waveguide is rarely available. A new approach to identifying the ionospheric exit points of the magnetospheric whistler mode emissions is presented, which takes into account the observed wave polarization. The method relies on the initial circular polarization of the ducted magnetospheric emissions which is shown to convert to linear polarization after propagation in the earth-ionosphere waveguide at a predictable rate. Finite-difference time domain modeling of observed eccentricity provides a metric for determining distance from observer to ionospheric exit point. The method is shown to produce good agreement with observations of magnetospheric chorus emissions, artificially triggered emissions, and lightning-induced whistlers.

Microelectromechanical systems (MEMS) resonators serve as frequency selective components in applications ranging from biology to communications. In this paper, the dynamic behavior of an RF MEMS disk resonator is formulated using an analytical method.

Microelectromechanical systems (MEMS) resonators serve as frequency selective components in applications ranging from biology to communications. In this paper, the dynamic behavior of an RF MEMS disk resonator is formulated using an analytical method.

This paper presents high-order (HO) electromagnetic modeling of plasmonic nanostructures based on the Locally Corrected Nystrom (LCN) method. Advanced nanophotonic and nanoplasmonic structures involve electrically large electromagnetic structures that are very complex in both geometry and material composition. Hence, advanced analysis and design tools are required in order to predict the performance of such structures and optimize the geometrical parameters prior to costly prototype development. In this perspective, the LCN is exploited to solve the electromagnetic scattering of plasmonic nanostructures. The LCN utilizes basis functions of higher orders defined on large geometrical elements, which significantly reduces the number of unknowns for a given problem. Compared to other well-known methods for EM modeling of plasmonic nanostructures, the LCN is computationally efficient, straightforward to implement and provides exponential convergence. A full comparison, in terms of time and complexity between the proposed method and previous works for a few 3D nanoplasmonic structures are presented to validate the accuracy, efficiency and flexibility of the proposed method to simulate the behavior of electromagnetic fields in real nanoplasmonic problems.

It is demonstrated that the Locally Corrected Nyström (LCN) method is a versatile and numerically efficient computational method for the modeling of scattering from plasmonic bowtie nanoantennas. The LCN method is a high-order analysis method that can provide exponential convergence. It is straightforward to implement, accurate and computationally efficient. To the best of the author's knowledge, the high-order LCN is here applied for the first time to 3D nanostructures. Numerical results show the accuracy and efficiency of the LCN applied to the electromagnetic analysis of nanostructures.

A well-conditioned, high-order Nyström discretization of a volume integral equation for quasi-magnetostatic, time-harmonic eddy current analysis of magnetic-conducting materials is presented. Good conditioning is contingent on augmenting the system with a charge neutrality constraint. Two forms of the continuity constraint are discussed. An iterative diagonal preconditioning scheme is applied to greatly improve the condition number. Results are presented for canonical problems and the TEAM Workshop Problem 7.

Data sparse direct solution methods for electromagnetic simulation problems have proven to be useful for a number of situations, both as standalone direct solvers and as general purpose preconditioners for use with iterative solvers. One set of such direct methods is provided by the LOGOS framework, which is based on expanding the underlying system matrix in a basis of local solutions that satisfy global boundary conditions. A particular subset of the LOGOS-based solution methods is referred to as the overlapped, localizing (OL) LOGOS method. This approach to factoring the system matrix is based on expanding the system matrix in a basis of overlapping sources that localize the scattered field to a spatial region that is also covered by the source functions. It has previously been shown that the computational complexity of such factorizations can scale as well as O(N log N) for low to moderate frequencies when used as a direct solver. The OL-LOGOS method has also been shown to provide an effective, O(N log N) general purpose preconditioner when used to factor the near-neighbor matrix obtained from the multilevel fast multipole method algorithm.

A quasi-magnetostatic volume integral equation discretized using the Nyström method is presented. The integral equation is formulated in terms of the differential susceptibility for use in hysteresis modeling. A simple stepped algorithm for hysteresis modeling of non-linear magnetic materials is studied. The algorithm is investigated using two non-linear models: a unified hysteresis model and the Jiles-Atherton model. Results are presented for a magnetic sphere excited by an alternating field and the computed results compare well with analytic results. The algorithm also captures minor loops.

A method is proposed for solving the time-dependent Maxwell's equations via the discontinuous Galerkin finite-element time-domain (DGFETD) method with dispersive media. An auxiliary differential equation (ADE) method is used to represent the constitutive relations. The method is applied to Drude materials, as well as to multiple pole Debye and Lorentz materials. An efficient implementation for high-order Runge-Kutta time integration schemes is presented. The method is validated and is shown to exhibit high-order convergence.