Marco Pasquale

Marco Pasquale, Stefano Markidis

Jacobian-Free Newton-Krylov (JFNK) methods avoid forming the full Jacobian, but still require Jacobian-vector products, i.e., Gateaux derivatives of the nonlinear residual along Krylov directions. In standard Finite Differences (FD) formulations, these products are obtained by perturbing the Newton state and differencing residuals, making the linearization sensitive to round-off error and floating-point precision. This work evaluates the global impact of forward-mode Automatic Differentiation (AD) as a replacement for FD Jacobian-vector product in finite-precision JFNK solvers. The comparison keeps the discretization, Newton iteration, line search, Krylov methods, tolerances, and CPU/GPU backend fixed, only varying linearization strategy. Benchmarks include Burgers dynamics, Su-Olson radiation diffusion, reaction-diffusion, and nonlinear time-harmonic Maxwell equations, each evaluated in different nonlinear regimes. By preventing degradation of the Krylov operator, AD accelerates computation by 2-3 orders of magnitude across both CPU and GPU architectures. More importantly, it drastically improves global solver robustness, achieving a minimum completion rate of 95%, compared to just 42% for FD. Ultimately, accurate Gateaux derivatives unify performance and accuracy in JFNK methods, making AD the optimal choice for stiff nonlinear and reduced-precision environments.

Marco Pasquale, Erik M. Åsgrim, Stefano Markidis et al.

Optimizing Reconfigurable Intelligent Surfaces (RIS) is a high-dimensional combinatorial challenge. Current quantum algorithms often simplify this problem by ignoring physical constraints like mutual coupling, which significantly degrades real-world performance. Rather than targeting a fully realistic RIS description, we embed progressively more physics-informed models of mutual coupling into Quadratic Unconstrained Binary Optimization (QUBO) formulations. We evaluate four Ising interaction models ($J_{ij}$) for the Quantum Approximate Optimization Algorithm (QAOA), ranging from idealized phase-only to fully dense physical models. Analyzing a $5 \times 5$ grid, our results expose a critical trade-off between spatial pointing accuracy and quantum hardware feasibility. While complete global coupling maximizes beamforming precision, dense Hamiltonians introduce prohibitive routing overhead and complicate convergence on near-term processors. Ultimately, we demonstrate that while physics-informed quantum optimization is mathematically viable, sparse, distance-penalized models remain a necessary compromise for execution on current noisy intermediate-scale quantum (NISQ) devices.

Marco Pasquale, Andong Hu, Luca Pennati et al.

As computational complexity in electromagnetics increases with frequency, full-wave solvers become computationally infeasible for electrically large problems. To address this limitation, we present a shooting and bouncing rays (SBR) method for efficiently modeling electromagnetic backscattering of metallic objects in the high-frequency regime. The method couples multi-reflection geometrical-optics ray transport with a physical optics surface integral discretized over ray tubes. To reduce the massive ray-surface intersection search space, we use a bounding volume hierarchy (BVH) and organize the computation as a trace-integrate pipeline. The ray tracing generates hit data, and the physical optics integral is evaluated over valid intersections only. Numerical accuracy is controlled through an incident-ray sampling rule that mitigates phase aliasing in the discretized physical optics integration. The method is accelerated on NVIDIA and AMD GPUs and parallelized with MPI. We validate against analytical Mie solutions for a perfectly electrically conducting (PEC) sphere and demonstrate applicability to a complex aircraft geometry for monostatic radar cross-section prediction.