WIPL-D 2D Solver

WIPL-D 2D Solver is intended for numerical electromagnetic analysis of cylindrical structures, theoretically infinitely long. The program works with 2D cross-sections (cuts) of the analyzed structure.


WIPL-D 2D Solver is integrated with WIPL-D Pro (3D surface-modeling tool) and WIPL-D Pro CAD (3D solid-modeling tool), so that arbitrary cross-section from a 3D model with material specifications can be easily extracted for 2D electromagnetic analysis. An example of a complex 3D structure with incorporated tool for extraction of cuts is shown in the header image. It shows how the cut is extracted from the model of a fighter airplane, while the corresponding imported cut in 2D is shown in the image below.

Example of a 2D cross-section (cut) automatically obtained from a complex 3D geometry

The tool is also seamlessly integrated with WIPL-D Optimizer, which allows simultaneous optimization of arbitrary number of the EM structure parameters in the same way as in WIPL-D Pro or WIPL-D Pro CAD. Time-Domain Solver, another WIPL-D tool which can be used with WIPL-D 2D Solver, allows calculation of time-domain response from the results obtained in frequency domain. WIPL-D Sweeper is also available through 2D Solver's interface.

The Engine

Numerical engine is based on surface integral equation formulation: electric field integral equations (EFIE) for metallic structures and PMCHWT formulation for dielectric and magnetic materials. It can handle arbitrary combinations of piecewise linear materials along with any combination of infinitely or finitely thin layers with distributed loadings. Every parameter, including material and distributed loading specifications can be frequency dependent.

WIPL-D 2D Solver uses both in-core (matrix in RAM) and out-of-core (matrix at hard disks) matrix factorization algorithms. For in-core solution with 32 GB of RAM, analysis of cross-sections up to 6,000 wavelengths can be done in matter of hours. State-of-the-art out-of-core solver accelerated with graphical processing units (GPUs) allows analysis of cross-sections up to 150,000 wavelengths in 24 hrs on a single desktop PC with up to 3 GPUs (for the further details of the supported hardware contact WIPL D).

Application areas

WIPL-D 2D Solver deals with scattering simulations. It calculates surface electric and magnetic currents at the material discontinuities, near electric and magnetic field, far (scattered) field and radar cross section (RCS). An example of a 2D cross-section, which represents a PEC elliptical scatterer, is shown in the image below, along with the results for near field in its vicinity. Also, an example of radar cross-section (RCS) normalized to the wavelength in free space is shown afterwards.

Model of a structure with elliptical cross-section in WIPL-D 2D Solver

Near-field calculated with WIPL-D 2D Solver

An example of RCS calculated with WIPL-D 2D Solver

As an illustration of WIPL D 2-D capabilities, a 12-decade frequency sweep of backscattered RCS from a perfectly conducting cylinder with circular cross-section of radius 1 m, is shown in the figure that follows. The sweep is performed so that at lowest frequency (~5 Hz) the circumference is λ/10,000,000, while at the highest frequency (~500 GHz) the circumference is 10,000 λ. Presented results are obtained with numerical MoM analysis (in-core), on a computer with 32 GB RAM . The Rayleigh region, MIE region (zoomed-in) and the physical optics region can all be seen.

Back-scattering from circular cylinder of radius 1 m: sweep from
electrically small (λ/10,000,000) to electrically large cross-section (10,000 λ)