**Table of Contents**

## Input Examples

### A complete example for a lossless cavity

ModelInfo: { File: dds3.ncdf //mesh file. It is the file converted using acdtool BoundaryCondition: { //specify boundary conditions. The numbers here are sideset in cubit Magnetic: 1, 2 //reference surfaces 1 and 2 are symmetric planes Electric: 3 4 //set reference surfaces 3 and 4 to be electric boundary condition Exterior: 6 //surface group 6 (maybe many surfaces) is metal } SurfaceMaterial: { //for each metal (exterior) surface group, list the sigma values ReferenceNumber: 6 Sigma: 5.8e7 } } FiniteElement: { Order: 2 //set the finite element basis function order to be used. CurvedSurfaces: on } EigenSolver: { NumEigenvalues: 1 //want to compute 1 mode FrequencyShift: 10.e9 //the eigenfrequency of the mode should be above 10GHz }

Once Omega3P run is successfully completed, eignvectors are stored in subdirectory <tt>eigens</tt>. User can convert them to mode files to be visualized using paraview. The following is the command to do that:

acdtool postprocess eigentomode eigens

### A complete example about a cavity with lossy materials

ModelInfo: { File: ./pillbox.ncdf BoundaryCondition: { Electric: 1,2,3,4 Exterior: 6 } Material : { Attribute: 1 Epsilon: 1.0 Mu: 1.0 } Material : { Attribute: 2 Epsilon: 1.0 Mu: 1.0 EpsilonImag: -0.2 //lossy material } } FiniteElement: { Order: 1 Curved Surfaces: off } EigenSolver: { NumEigenvalues: 2 FrequencyShift: 5e9 }

### A complete example with periodic boundary conditions

ModelInfo: { File: c026ds-pbc.ncdf BoundaryCondition: { Magnetic: 1 2 Periodic_M: 3 //master surface Periodic_S: 4 //slave surface, the mesh should be exactly same as those on the master surface Exterior: 6 Theta: -150 //phase } } FiniteElement: { Order: 2 CurvedSurfaces: on } EigenSolver: { NumEigenvalues: 1 FrequencyShift: 10e9 }

### A complete example with waveguide loaded cavity

ModelInfo: { File: cell1fourth.ncdf BoundaryCondition: { Magnetic: 1,2,3,4 Exterior: 6 Waveguide: 7 //Automatic numerical waveguide port solution will be generated per default //Absorbing: 7 //First-order absorbing boundary condition. Default cutoff is 0 } } FiniteElement: { Order: 1 Curved Surfaces: on } EigenSolver: { NumEigenvalues: 1 FrequencyShift: 9.e9 } Port: { ReferenceNumber: 7 NumberOfModes: 3 // this whole 'Port' container is only needed if you want to load more than 1 mode on a port //CutoffFrequency: 5.6e9 // this is only for Absorbing boundary conditions specified above. Can be used to have the same cutoff as another waveguide mode for faster solution }

## Analytic Ports (for polarization)

Omega3p normally uses a numerical solution for each port but if you need to specify the polarization of the waveguide you can give an analytic solution instead.

From the last example we could have used:

Port: { ReferenceNumber: 7 //this number should match surface groups in waveguide boundary condition. Origin: 0.0, 0.0415, 0.0 //the origin of the 2D port in the 3D coordinate system XDirection: 1.0, 0.0, 0.0 //the x axis of the 2D port in the 3D coordinate system YDirection: 0.0, 0.0, -1.0 //the y axis of the 2D port in the 3D coordinate system ESolver: { Type: Analytic //analytic expression is used Mode: { WaveguideType: Rectangular //it is a rectangular waveguide ModeType: TE 1 0 //load the TE10 mode A: 0.028499 //dimension of the waveguide in x B: 0.0134053 //dimension of the waveguide in y } } }

### Load TEM mode in a coax waveguide

Port: { ReferenceNumber: 2 Origin: 0.0, 0.0, 0.011 ESolver: { Type: Analytic Mode: { WaveguideType: Coax ModeType: TEM A: 0.0011 //smaller radius B: 0.0033 //larger radius } } }

### Load TE11 mode in a circular waveguide

Port: { ReferenceNumber: 2 Origin: 0.0, 0.0, 0.1 XDirection: 1.0, 0.0, 0.0 YDirection: 0.0, 1.0, 0.0 ESolver: { Type: Analytic Mode: { Waveguide type: Circular Mode type: TE 1 1 A: 0.03 } } }

### Load two TE modes in the same rectangular waveguide

Port: { Reference number: 9 // FPC Origin: 0.0, 0.198907, -0.4479152585 XDirection: -1.0, 0.0, 0.0 YDirection: 0.0, 0.0, 1.0 ESolver: { Type: Analytic Mode: { WaveguideType: Rectangular ModeType: TE 1 1 A: 0.1348935946 B: 0.024973714999999970 } } } Port: { Reference number: 9 // FPC Origin: 0.0, 0.198907, -0.4479152585 XDirection: -1.0, 0.0, 0.0 YDirection: 0.0, 0.0, 1.0 ESolver: { Type: Analytic Mode: { WaveguideType: Rectangular ModeType: TE 2 0 A: 0.1348935946 B: 0.024973714999999970 } } }

LinearSolver options in EigenSolver container

- The first option is that user does not provide anything. The EigenSolver container in the input file looks like:
In this case, Omega3P will use the default option for linear solver for solving shifted linear systems
EigenSolver: { NumEigenvalues: 1 FrequencyShift: 10.e9 Tolerance: 1.e-8 }

- The second option is to use float version of the sparse direct solver.
EigenSolver: { NumEigenvalues: 1 FrequencyShift: 10.e9 Preconditioner: MUMPSFLOAT //use the float version. memory usage reduced into half. }

- The third option is to use Krylov subspace method with different preconditioner.
The code will choose either CG (real matrices) or GMRES (complex matrices) and the p-version
EigenSolver: { NumEigenvalues: 1 FrequencyShift: 10.e9 Preconditioner: MP //this use p-version of multilevel preconditioner. }

of multilevel precondtioner as the solver for shifted linear systems.

## FAQ

### How to calculate Wallloss Quality Factor?

There are two ways to do so. Each way has its advantage and disadvantage.

- Inside ModelInfo.BoundaryCondition define a set of boundary surfaces as Exterior.

For each of the boundary surfaces, have a corresponding SurfaceMaterial container inside ModelInfo.

For example:After you run omega3p with the input file, you will get a file called "output" under the same directory. Inside the file, it has a summary of results such as:ModelInfo: { File: .dds3.ncdf BoundaryCondition: { Magnetic: 1, 2, 3, 4 Exterior: 6 // sideset 6 is defined as Exterior BC. } SurfaceMaterial: { // have a separate for each number in Exterior BC ReferenceNumber: 6 //the corresponding sideset in Exterior BC Sigma: 5.8e7 //electrical conductivity of the material } }

The number after QualityFactor is the one you are looking for. This method uses perturbation theory and has advantage that it is very simple. The computation associated with it is minimal.Mode : { TotalEnergy : 4.4270939088102e-12 QualityFactor : 6478.5096350252 File : ./dds.l0.1.144469E+10.m0 PowerLoss : 4.9139118623939e-05 Frequency : 11444685657.626 }

- Inside ModelInfo.BoundaryCondition, define the set of surfaces as Impedance (instead of Exterior in method 1).

Set the HFormulation to be 1 (this is very important). Also, have a set of corresponding SurfaceMaterials inside ModelInfo as those in method 1. For example:After you run omega3p with the input, in the output file, you will seeModelInfo: { File: dds3.ncdf BoundaryCondition: { HFormulation: 1 Magnetic: 1, 2, 3, 4 Impedance: 6 } SurfaceMaterial: { ReferenceNumber: 6 Sigma: 5.8e7 } }

The number after ExternalQ is the wall loss Q you are looking for. During the omega3p run, it should also print out the Q information such asMode = { TotalEnergy = { 6.2827077634198e-07, 0 }, ExternalQ = 6579.1486638005, QualityFactor = inf, File = './dds.l0.R1.144619E+10I8.698837E+05.m0', PowerLoss = 0, Frequency = { 11446188331.641, 869883.69746227 } }

Note that this method set an impedance boundary condition on those surfaces and make the eigenvalue problem complex and nonlinear. It takes more time and memory to solve the problem. But the field will be in the right phase (even close to the boundary surfaces).COMMIT MODE: 0 FREQ = (11446188331.64141,869883.6974622669) k = (239.8943683519209,0.01823141417003215) Q = 6579.148663800495

Both methods should give you converged Q results if mesh is dense enough.