## MDD (Multilevel Domain Differentiated)

# MDD (Multilevel Domain Differentiated)

## Product By :

### ISMB (Istituto Superiore Mario Boella)

http://www.ismb.it/en/Advanced_Computing_and_Electromagnetics

### POLITO (Politecnico di Torino)

## Scope :

The general aim of MDD is the numerical computation of the EM response of metallic 3D objects, based on their surface description. The 3D objects can have overall sizes of many wavelengths and levels of detail from very moderate to extending over the whole structure.

## Features :

Analysis of electrically large 3D objects and in particular of complex geometries, including sub-wavelength details. In particular, the tool aims at “high-fidelity” modeling, i.e. via analysis of the CAD model without any human (or automatic) effort to “clean” the original CAD of details. This is achieved via a specialized preconditioning method, based on a Multi-Resolution system of basis functions. It is easily interfaced with MoM-based codes because the proposed basis is a linear combination of the standard MoM basis functions. Its properties are also compatible with the complexity and memory scaling of (multilevel) fast MoM approaches.

*The module, which belongs to the family of Frequency Domain (FD) methods, supports:*

- Surface discretizations with triangular mesh, and wires discretizations with linear mesh elements;
- Plane wave (see Figure 2) and voltage gap excitations;
- Surface impedance modeling of thin sheet of dielectrics/composite materials;
- A FFT-based fast solver, able to routinely solve problems up to 1 Million unknowns on standard

workstations (and up to 10 Millions unknowns on large systems); - An efficient multiscale preconditioner able to solve low-frequency problems down to 1 Hz

*Typical outputs (Figure 3) of the tool are :*

- Electric current density on the input mesh (see Figure 4 and Figure 5);
- Far field pattern;
- Electric and magnetic field intensity in a set of points defined by the user; the field locations are

completely arbitrary (close to the surface, exactly on the surface, inside closed cavities). See Figure

5-b for an example of field intensity on a cut plane.

## Screenshots :

**Figure 1: Overview of the module MDD inside the framework.**

**Figure 2: plane wave definition inside the framework.**

**Figure 3: Input window to configure the “Output request” in the framework.**

**Figure 4: Morphed P180 aircraft model, meshed with 1’086’083 unknowns: surface current density. (a) top view**

** of surface current at 300 kHz. The incident direction of the plane wave is ( θ ^{i} = 90° , φ^{i} = 225° ) (b) details of the**

**equipment and seats inside the aircraft (c) details of the nose.**

** **

** Figure 5: Morphed EV55 aircraft: surface current density at 244 MHz (A) side view of details of the equipments and seats in the aircraft; (B) electric field distribution on a cut plane.**