CTC-AR77: Certified, Goal-Oriented Adaptive PSTD Simulation of a 77 GHz Automotive Radar behind a Bumper Fascia — Benchmarks, Negative Results, a Frozen Core and its C++/GPU Port

A bumper fascia in front of a 77 GHz radar shifts the monopulse boresight by degrees, and measured fascia-induced angle errors of 0.1 ◦ –0.3 ◦ are large enough to matter for lane assignment. We built an open benchmark for simulating this effect, CTC-AR77, and an adaptive pseudospectral time-domain (PSTD) solver that sizes the computational box and the grid spacing along each axis during the run, with a homotopy (winding-number) certificate that localizes the boresight null. This paper reports the whole path: the benchmark and its physics, eleven bugs and false hypotheses found along the way, sixteen experiments (e17–e26), and what survived. The controller found an expert-quality anisotropic grid automatically: on a 15 ◦ -tilted 3 mm fascia it matched the far-field pattern of a hand-tuned anisotropic grid at 53.5% of the reference cost (rule: 73.3%), and a two-pass variant reached 0.002 ◦ boresight error at 58.2%. Feature indicators failed (gradient “contrast” and global spectral tails were blind to the fascia); a goaloriented policy with an indicator-free calibrated grid met an angle tolerance of 0.02 ◦ in all eight held-out scenarios at 42% of the reference cost. A sweep of the absorbing boundary showed that the 12-cell PML used by every reference is itself wrong by up to 0.024 ◦ on tilted fascias, because waves guided in the fascia reach the side walls at grazing incidence; the reference fails the angle tolerance at 25 ◦ . An end-to-end test of all layers against a tighter reference selected a frozen core (CF-1.0): one calibrated grid for both goals, a PML chosen from the fascia tilt before the run, FFT-friendly sizes, a reference-free null-index certificate, and a policy that reports but never escalates. It meets both goals in all four acceptance scenarios at 70.9% of the reference cost with the largest boresight error at half the tolerance. Its C++ port (FFTW, OpenMP) reproduces the Python reference to 10 −14 degrees and is 4.1× faster end to end on two cores; 1.76× of that comes from FFT-friendly grid sizes alone. A VkFFT GPU backend is written, verified in its dataflow, and not yet run on a GPU. All numerical errors are 40–100 times below receiver-noise and interference floors. We state plainly what is not claimed: no state of the art was broken, and no comparison with commercial solvers was made.