# PDESolverOptions Properties

Algorithm options for solvers

A PDESolverOptions object contains options used by the solvers when solving a structural, thermal, or general PDE problem specified as a StructuralModel, ThermalModel, or PDEModel object, respectively. StructuralModel, ThermalModel, and PDEModel objects contain a PDESolverOptions object in their SolverOptions property.

Solvers for structural modal analysis problems and reduced-order modeling use the Lanczos algorithm.

## Statistics and Convergence Report

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Flag to display the internal solver statistics and the convergence report during the solution process, returned as 'off' or 'on'.

Example: model.SolverOptions.ReportStatistics = 'on'

Data Types: char

## ODE Solver

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Absolute tolerance for the internal ODE solver, returned as a positive number. Absolute tolerance is a threshold below which the value of the solution component is unimportant. This property determines the accuracy when the solution approaches zero.

Example: model.SolverOptions.AbsoluteTolerance = 5.0000e-06

Data Types: double

Relative tolerance for the internal ODE solver, returned as a positive number. This tolerance is a measure of the error relative to the size of each solution component. Roughly, it controls the number of correct digits in all solution components, except those smaller than thresholds imposed by AbsoluteTolerance. The default value corresponds to 0.1% accuracy.

Example: model.SolverOptions.RelativeTolerance = 5.0000e-03

Data Types: double

## Nonlinear Solver

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Acceptable residual tolerance for the internal nonlinear solver, returned as a positive number. The nonlinear solver iterates until the residual size is less than the value of ResidualTolerance.

Example: model.SolverOptions.ResidualTolerance = 5.0000e-04

Data Types: double

Maximal number of Gauss-Newton iterations for the internal nonlinear solver, returned as a positive integer.

Example: model.SolverOptions.MaxIterations = 30

Data Types: double

Minimum damping of the search direction for the internal nonlinear solver, returned as a positive number. For details, see Nonlinear Solver Algorithm.

Example: model.SolverOptions.MinStep = 1.5259e-7

Data Types: double

Type of norm for computing the residual for the internal nonlinear solver, returned as Inf, -Inf, a positive number, or 'energy'.

The infinity norms of a vector are

${‖\rho ‖}_{\infty }={\mathrm{max}}_{i}\left(|\rho \left(i\right)|\right)$

${‖\rho ‖}_{-\infty }={\mathrm{min}}_{i}\left(|\rho \left(i\right)|\right)$

The Lp-norm of a vector ρ that has N elements is

${‖\rho ‖}_{p}=\frac{{\left[\sum _{k=1}^{N}{|{\rho }_{k}|}^{p}\right]}^{\frac{1}{p}}}{{N}^{\frac{1}{p}}}$

The energy norm of a vector ρ is

$‖\rho ‖={\rho }^{T}K\rho$

Here, K is the combined stiffness matrix defined in Nonlinear Solver Algorithm.

Example: model.SolverOptions.ResidualNorm = 'energy'

Data Types: double | char

## Lanczos Solver

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Maximum number of Lanczos shifts, specified as a positive integer. Increase this value when computing a large number of eigenpairs.

Example: model.SolverOptions.MaxShift = 500

Data Types: double

Block size for block Lanczos recurrence, specified as a positive integer. The default number ranges from 7 to 25, depending on the size of the stiffness matrix K.

Example: model.SolverOptions.BlockSize = 20

Data Types: double

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