The 3D Maxwell Project

Setup

Software dependencies:

• Dealii 9.3.
• Petsc with complex doubles as number type.
• Mumps (as a dealii dependency)

Have to delete the content of the function project_matrix_free in vector_tools_project.templates.h in DealInstall/include/deal.II/numerics/

Before the first run, one dependency has to be fetched. To do so, navigate a terminal to the main folder of the repo. Then run the commands git submodule init and git submodule update. This will clone the gtest framework into the third_party folder. Afterwards, create a folder called build in the main folder, enter it and run cmake. I.e.

git submodule init
git submodule update
mkdir build
cd build
cmake ..

Introduction

This code was developed by Pascal Kraft in an effort to generate a fast code to compute optimal shapes of 3D-waveguides based on a solution of the full Maxwell-Problem without simplifications based on non-physical assumptions.

Core elements are a refined adjoint based optimization scheme and a sweeping preconditioner.

This is a work in progress and not currently ready for general usage. Please refer to pascal.kraft@kit.edu for more information.

There are currently works in the branch complex-numbers that might need to be pulle.

Naming convenctions

Expression	Meaning
Sector	A sector is an expression used in shape modeling and refers to a subdomain between the connectors.
Layer	used in the implementation and represents the part of the triangulation owned by one Process.
Connector	The structure in the two halfspaces towards z->\infty and z->-\infty outside of the computational domain.
...	...

Levels in Hierarchical Sweeping

There are 2 level types: global and local.

Global

The global level describes how many hierarchical levels there are in total.

• 0: purely local computation, no sweeping.
• 1: there is only sweeping in the z direction.
• 2: there is sweeping in the z direction and the blocks are solved by sweeping in the y direction
• 3: there is sweeping in the z direction and the blocks are solved by sweeping in the y direction. The blocks required in the y-sweep are solved by sweeping the x-direction.

Local

It makes a difference for which of the sweeps a matrix is assebled and what the global sweeping level is. The local level describes for which scenario the block is assembled. It counts from 0 up. 0 means that we assemble a local block, i.e. a direct solver for the local problem with sweeping in only one direction. If local is 0 and global is 1, there is only sweeping in the z-direction. That means the local block is assembled by cutting off the x- and y- directions. If local is 0 and global is 2, the lowest order sweeping is in the y-direction, so the direct solver is assembled for a domain with boundary conditions in x- and z-direction but sweeping in y (similar for local 0 and global 3, only for x). If local is 1 or higher, the block is not assembled for a direct solver but a matrix for GMRES is built. This means that not all surfaces are either boundaries with HSIE or sweeping block interfaces (Dirichlet boundaries), they can now be internal.

Rotations for surface extraction

For boundary id:

b_{id}	x	y
0	z	y
1	z	y
2	x	z
3	x	-z
4	-x	y
5	x	y

Predefined waveguide shapes

This code comes with some example cases called the waveguide hump examples. These examples are available as hdf5 and obj files in the folder Modes -> PWB_Bond_Trajectories. The first three cases are numbered 0,1 and 2 and then continue on at 40, 41, ... , 72. In total there are 3 + 33 cases, so 36. To run these, a parameter in the case file can be used. Be carefull, however, because these numbers start at 0 and count to 35. The table below lists how these numbers correlate:

PWB Bond index	Predefined case number	Approximate signal loss in %	Approximate signal loss in db
0	0
1	1
2	2
40	3
41	4
42	5
43	6
44	7
45	8
46	9
47	10
48	11
49	12
50	13
51	14
52	15
53	16
54	17
55	18
56	19
57	20
58	21
59	22
60	23
61	24
62	25
63	26
64	27
65	28
66	29
67	30
68	31
69	32
70	33
71	34
72	35

Thanks

My thanks go to the CRC 1173 which is funding my research. I also thank the team behind the deal.II library that has been the basis for my implementations.