arXiv subjects

Vladimir Okhmatovski

Publications and source records attributed to Vladimir Okhmatovski.

4 recordsLinked to original sources

arXiv2026

TT-FDTD: Tensor Train Accelerated Three-Dimensional FDTD With Logarithmic Cost of Spatial Operators

Quantized tensor-train (QTT) compression is incorporated into a full-vector three-dimensional scattered-field finite-difference time-domain (FDTD) formulation on uniform Yee grids. All six electromagnetic-field components, material-dependent update coefficients, equivalent-current sources, and staggered finite-difference operators are represented in compatible QTT form. Gaussian regularization of voxelized material interfaces is used to reduce the coefficient ranks generated by abrupt dielectric and conductivity transitions. The formulation is evaluated for an anatomically heterogeneous human-head model and a homogeneous dielectric sphere on grids containing up to $512^3$ spatial cells. The reported results show that interface smoothing substantially reduces material-coefficient ranks and that the TT--FDTD solution reproduces the full-grid transient fields with pointwise absolute errors on the order of $10^{-4}$ in the examined slices. Compared with conventional FDTD, the tensor representation greatly reduces storage at fine discretizations, although tensor contractions and recompression introduce additional per-step computational cost. These results demonstrate the feasibility and memory--time tradeoff of QTT-accelerated three-dimensional FDTD for large structured-grid simulations.

physics.comp-ph↗

arXiv2026

Curl-based Electric-Field Boundary Condition for the Accurate and Stable Electromagnetic Scattering Analysis

We introduce a curl-based Electric-Field Integral Equation (Curl-EFIE) for the electromagnetic scattering analysis from perfect electric conductors. The formulation is derived by enforcing a vanishing curl on the EFIE over the boundary manifold, achieved by testing the internal electric field with orthogonal tangent solenoidal disks. We demonstrate that a Method-of-Moments (MoM) discretization of the Curl-EFIE converges to a Galerkin-discretized MFIE as the testing disk dimensions vanish, yielding stable, breakdown-free impedance matrices for low frequencies and dense grids. Unlike the strongly singular kernels of the MFIE, the Curl-EFIE utilizes weakly singular kernels, significantly simplifying source integral evaluations. As a first-kind integral equation, it bypasses the MFIE's Gram matrix requirement, facilitating the analysis of non-matching triangulations. Furthermore, a linear combination of the Curl-EFIE and the conventional EFIE provides an interior-resonance-free formulation analogous to the Combined Field Integral Equation (CFIE). Finally, the Curl-EFIE performs particularly well at capturing the scattering behavior of sharp- edged and cornered geometries.

physics.comp-ph↗

arXiv2024

H-Matrix Accelerated Direct Matrix Solver for Maxwell's Equations using the Chebyshev-based Nyström Boundary Integral Equation Method

An H-matrix accelerated direct solver employing the high-order Chebyshev-based Boundary Integral Equation (CBIE) method has been formulated, tested, and profiled for performance on high contrast dielectric materials and electrically large perfect electric conductor objects. The matrix fill performance of the CBIE proves to be fast for small to moderately sized problems compared to its counterparts, e.g. the locally corrected Nyström (LCN) method, due to the way it handles the singularities by means of a global change of variable method. However, in the case of electrically large scattering problems, the matrix fill and factorization still dominate the solution time when using a direct solution approach. To address this issue, an H-Matrix framework is employed, effectively resolving the challenge and establishing the CBIE as a competitive high-order method for solving scattering problems with poorly conditioned matrix equations. The efficacy of this approach is demonstrated through extensive numerical results, showcasing its robustness to problems that are electrically large, near physical resonances, or that have large dielectric permittivities. The capability of the proposed solver for handling arbitrary geometries is also demonstrated by considering various scattering examples from complex CAD models.

math.NA↗

arXiv2021

SuperVoxHenry Tucker-Enhanced and FFT-Accelerated Inductance Extraction for Voxelized Superconducting Structures

This paper introduces SuperVoxHenry, an inductance extraction simulator for analyzing voxelized superconducting structures. SuperVoxHenry extends the capabilities of the inductance extractor VoxHenry for analyzing the superconducting structures by incorporating the following enhancements. 1. SuperVoxHenry utilizes a two-fluid model to account for normal currents and supercurrents. 2. SuperVoxHenry introduces the Tucker decompositions to reduce the memory requirement of circulant tensors as well as the setup time of the simulator. 3. SuperVoxHenry incorporates an aggregation-based algebraic multigrid technique to obtain the sparse preconditioner.

cs.CE↗