Define the element types.

Specify material properties.

Define the model geometry.

Mesh the model into elements.

Enter SOLUTION.

Define the analysis options. Choose any of three options to solve the simultaneous equations generated by a p-method analysis. These solvers are discussed at length in "Solution" in the Basic Analysis Guide.

To specify the type of equation solver, issue one of the following:

We generally recommend that you use the JCG solver for a p-element analysis. For most 3-D solid models and for very large 2-D models (usually greater than 40,000 DOF), the JCG solver is usually faster than the frontal solver.

In certain cases, such as when your model contains elements with high aspect ratios or material type discontinuities, a greater number of iterations may be required to achieve convergence for the PCG solver. You may increase the maximum number of iterations by using the MULT option on the EQSLV command. This option is only valid when solving with the PCG solver. See the EQSLV command description in the Commands Reference for more information on this capability.

For more information on the general use of the PCG solver, refer to "Solution" in the Basic Analysis Guide.

Apply the loads to the solid model (keypoints, lines, areas, etc.) or the finite element model (nodes and elements), except for inertia loads (gravity, rotational velocity, etc.), which are independent of the model. For a general discussion of solid model loads versus finite element loads, see "Loading" in the Basic Analysis Guide.

Loads Applicable to a p-Method Analysis

"Electrostatic Field Analysis (h-Method)" of this manual describes the loads applicable to an electrostatic analysis, including the commands associated with each type of loading.

Potential (VOLT) are DOF constraints that you would usually prescribe at a ground plane, a conductor, or at a far-field boundary. You can also use them to indicate symmetry boundary conditions.

Potential boundary conditions applied to all nodes of an element edge or face will also constrain the higher order potential variation along that edge or face.

You should not apply a potential only at a midside node. You may apply a potential at a corner node only.

Charge (CHRG) are point-wise loads that you would usually specify on a corner node.

Surface Charge Densities (CHRGS) are surface loads, also usually applied on the exterior of a body.

Volume Charge Densities (CHRGD) are body loads usually applied to elements.

Maxwell Surface Flag (MXWF) are flags indicating surfaces to compute forces. Surfaces of air elements adjacent to conductors or mechanical structures are usually flagged. Elements with flagged surfaces will have surface forces computed and stored. These forces can be reviewed in the postprocessor, or automatically transferred to a structural analysis (of the conductor or mechanical structure). The total “Global” force on a body may also be used as consequence criteria in the adaptive process.

You apply surface flags using the SF family of commands. Remember to apply these flags to electrostatic air elements adjacent to the conductor or mechanical body. In a pure electrostatic model, these conductors are not physically represented by elements so application of the surface flags is straightforward. In a multiphysics analysis, you can mesh the conductor region with finite elements which are inactive for the electrostatic run (using the 'null' element type (ET,,0). In this case, you can apply Maxwell surface flags by grouping the conductor elements into an element component (CM command) and calling the FMAGBC command macro.

The electrostatic p-elements output forces that are compatible with lower and higher order structural h-elements only. Transfer forces from the electrostatic analysis to a structural analysis by using the LDREAD command. Use element KEYOPT(7) for SOLID127 and SOLID128 to prescribe force computations for either lower order or higher order structural elements.

The structural p-elements (SOLID147 and SOLID148) do not support electrostatic-structural coupling.

Temperatures (TEMP) are applied to study the effects of temperature dependent permittivity. You can read in temperatures from a thermal analysis, or you can specify temperatures directly on the nodes or the solid model keypoints.

To obtain temperatures from a thermal analysis:

Specify load step options. The following solution options are available to aid in solving a p-Method analysis:

As mentioned earlier in this section, a p-method analysis works with a series of iterations, or p-loops, checking for convergence each time. The PPRANGE command is used to specify the overall range where the p-level may vary (somewhere between 2 and 8). For analyses beginning at p = 2, each element will have its solution checked for convergence against established criteria [PCONV]. If the solution is within the requested tolerance [PEMOPTS], that element will have its p-level held to 2. Those elements that did not converge within the specified criteria (that is, not fixed at p = 2 for the first iteration), will have their p-level increased, and another solution (iteration) will then be performed. At each iteration the convergence criteria (energy, potential, electric field, global forces, etc.) is checked, and if converged, the solution stops. Also, those elements whose individual solutions are considered to be converged will have their p-level held at the current p-level. This process is continued until all specified convergence criteria are met, or the maximum p-range has been reached.

Convergence Criteria Specifications

Convergence criteria may be global (for energy or surface Maxwell) forces) or local. Global energy is a good criteria to use when capacitance is the desired result. Electrostatic forces (Maxwell forces) on a body may be used as a convergence criteria. Forces are summed over all flagged surfaces to obtain a global force. This global force is then used as a convergence criteria.

Caution must be exercised when using the global force (EFORC) criteria. Since all flagged surface forces are summed, only a single body should be flagged. Otherwise, for more than one flagged body, the total force may be meaningless (or in fact, may sum to zero).

If you are specifically interested in the results at certain points in the model, then you should use local convergence criteria. Use this option to specify which areas of your model you would like to monitor for analysis convergence, as well as the type of criteria you would like to use to control convergence. Typically, you should select a few points of interest (nodes), at which to specify the convergence criteria (potential, electric field, etc.). In most cases, the default convergence tolerance (5%) is sufficient for generally good results. You may want to lower this tolerance if you require a more accurate solution. For a design study or optimization analysis, a higher tolerance will cut down on run times.

To set convergence values for p-method solutions, issue one of the following:

Specifications for Controlling p-levels

You may specify the starting (defaults to 2) and maximum (defaults to 8) p-levels that you wish to allow for your analysis [PPRANGE]. You may wish to start at a higher p-level if you have already completed an analysis and you want to perform a re-analysis (for a design change, for instance) and you know the final p-level where convergence will occur for most elements. You may also want to restrict the maximum p-level to less than 8 if conserving disk space or run time.

Accounting for Singularities

If the model contains any re-entrant (internal or concave) corners that are not modeled with a fillet radius, or contains point charges or any other areas of singularities, you should consider excluding these areas from the convergence computations. All elements that have a node at the singularity should be excluded.

To specify elements to be excluded from p-level escalations, issue one of the following:

You can reassign, or re-include, elements for convergence checking. You may determine which elements have been included or excluded by listing [PINCLUDE,STAT; PEXCLUDE,STAT; or *GET] or plotting elements [EPLOT]. Excluded elements will appear `whited-out' in the plot. You may also select included or excluded elements by issuing the ESEL command directly [ESEL,,PEXC or ESEL,,PINC] (no GUI equivalent). This facilitates using these elements as a component [CM].

To specify elements to be included in p-level escalations, issue one of the following:

Save a backup copy of the database.

Start the p-level iterations and solution process. The output will provide a summary of each loop, indicating the current p-level, the convergence statistics, and the status of how many elements have converged.