# solve

Solve structural analysis, heat transfer, or electromagnetic analysis problem

**Domain-specific structural, heat transfer, and electromagnetic workflows are not
recommended. New features might not be compatible with these workflows. For help
migrating your existing code to the unified finite element workflow, see Migration from Domain-Specific to Unified Workflow.**

## Syntax

## Description

solves the structural modal analysis problem represented by the finite element
analysis model `results`

= solve(`fem`

,FrequencyRange=`[omega1,omega2]`

)`fem`

for all modes in the frequency range
`[omega1,omega2]`

. Define `omega1`

as
slightly lower than the lowest expected frequency and `omega2`

as slightly higher than the highest expected frequency. For example, if the
lowest expected frequency is zero, then use a small negative value for
`omega1`

.

performs an eigen decomposition of a linear thermal problem represented by the
finite element analysis model `results`

= solve(`fem`

,DecayRange=`[lambda1,lambda2]`

)`fem`

for all modes in the
decay range `[lambda1,lambda2]`

. The resulting modes enable
you to:

Use the modal superposition method to speed up a transient thermal analysis.

Extract the reduced modal system to use, for example, in Simulink

^{®}.

obtains the modal basis of a linear or nonlinear thermal problem represented by
the finite element analysis model `results`

= solve(`fem`

,Snapshots=`Tmatrix`

)`fem`

using proper
orthogonal decomposition (POD). You can use the resulting modes to speed up a
transient thermal analysis or, if your thermal model is linear, to extract the
reduced modal system.

,
`results`

= solve(`fem`

,`tlist`

,ModalResults=`thermalModalR`

)

,
and
`results`

= solve(`fem`

,`tlist`

,ModalResults=`structuralModalR`

)

solve a transient thermal or structural problem or a frequency response
structural problem, respectively, by using the modal superposition method to
speed up computations. First, perform modal analysis to compute natural
frequencies and mode shapes in a particular frequency or decay range. Then, use
this syntax to invoke the modal superposition method. The accuracy of the
results depends on the modes in the modal analysis results.`results`

= solve(`fem`

,`flist`

,ModalResults=`structuralModalR`

)

returns the solution to the static structural analysis model represented in
`structuralStaticResults`

= solve(`structuralStatic`

)`structuralStatic`

.

returns the solution to the transient structural dynamics model represented in
`structuralTransientResults`

= solve(`structuralTransient`

,`tlist`

)`structuralTransient`

at the times specified in
`tlist`

.

returns the solution to the frequency response model represented in
`structuralFrequencyResponseResults`

= solve(`structuralFrequencyResponse`

,`flist`

)`structuralFrequencyResponse`

at the frequencies
specified in `flist`

.

returns the solution to the modal analysis model for all modes in the frequency
range `structuralModalResults`

= solve(`structuralModal`

,"FrequencyRange",`[omega1,omega2]`

)`[omega1,omega2]`

. Define `omega1`

as
slightly lower than the lowest expected frequency and `omega2`

as slightly higher than the highest expected frequency. For example, if the
lowest expected frequency is zero, then use a small negative value for
`omega1`

.

and
`structuralTransientResults`

= solve(`structuralTransient`

,`tlist`

,ModalResults=`structuralModalR`

)

solves a transient and a frequency response structural model, respectively, by
using the modal superposition method to speed up computations. First, perform
modal analysis to compute natural frequencies and mode shapes in a particular
frequency range. Then, use this syntax to invoke the modal superposition method.
The accuracy of the results depends on the modes in the modal analysis
results.`structuralFrequencyResponseResults`

= solve(`structuralFrequencyResponse`

,`flist`

,ModalResults=`structuralModalR`

)

returns the solution to the steady-state thermal model represented in
`thermalSteadyStateResults`

= solve(`thermalSteadyState`

)`thermalSteadyState`

.

returns the solution to the transient thermal model represented in
`thermalTransientResults`

= solve(`thermalTransient`

,`tlist`

)`thermalTransient`

at the times specified in
`tlist`

.

performs an eigen decomposition of a linear thermal model
`thermalModalResults`

= solve(`thermalModal`

,DecayRange=`[lambda1,lambda2]`

)`thermalModal`

for all modes in the decay range
`[lambda1,lambda2]`

. The resulting modes enable you
to:

Use the modal superposition method to speed up a transient thermal analysis.

Extract the reduced modal system to use, for example, in Simulink.

obtains the modal basis of a linear or nonlinear thermal model using proper
orthogonal decomposition (POD). You can use the resulting modes to speed up a
transient thermal analysis or, if your thermal model is linear, to extract the
reduced modal system.`thermalModalResults`

= solve(`thermalModal`

,Snapshots=`Tmatrix`

)

solves a transient thermal model by using the modal superposition method to
speed up computations. First, perform modal decomposition to compute mode shapes
for a particular decay range. Then, use this syntax to invoke the modal
superposition method. The accuracy of the results depends on the modes in the
modal analysis results.`thermalTransientResults`

= solve(`thermalTransient`

,`tlist`

,ModalResults=`thermalModalR`

)

returns the solution to the electrostatic, magnetostatic, or DC conduction model
represented in `emagStaticResults`

= solve(`emagmodel`

)`emagmodel`

.

returns the solution to the harmonic electromagnetic analysis model represented
in `emagHarmonicResults`

= solve(`emagmodel`

,Frequency=`omega`

)`emagmodel`

at the frequencies specified in
`omega`

.

## Examples

## Input Arguments

## Output Arguments

## Tips

When you use modal analysis results to solve a transient structural dynamics model, the

`modalresults`

argument must be created in Partial Differential Equation Toolbox™ from R2019a or newer.For a frequency response model with damping, the results are complex. Use functions such as

`abs`

and`angle`

to obtain real-valued results, such as the magnitude and phase.

## Version History

**Introduced in R2017a**