mphmatrix

str = mphmatrix(model,soltag,'Out',{'A'},...) returns a MATLAB® structure str containing the matrix A assembled using the solver node soltag and accessible as str.A, A being taken from the Out property list.

str = mphmatrix(model,soltag,fname,'Out',{'A','B',...}) returns a MATLAB structure str containing the matrices A, B, … assembled using the solver node solname and accessible as str.A and str.B, A and B being taken from the Out property list.

The function mphmatrix accepts the following property/value pairs:

Table 6-15: Property/Value Pairs for the mphmatrix command
Property	Expression	Default	Description
complexfun	on \| off	off	Use complex-valued functions with real input
eigname	String	lambda	Eigenvalue name
eigref	Double	0	Value of eigenvalue linearization point
extractafter	Solution feature tag	First dependent variable node	Specify at which point to extract the matrices
initmethod	init \| sol	init	Use linearization point
initsol	String \| zero	Active solver tag	Solution to use for linearization
matherr	on \| off	on	Error for undefined operations
nullfun	flnullorth \| flspnull \| flexplicit \| auto	auto	Null-space function
out	Cell array of strings		List of matrices to assemble
rowscale	on \| off	on	Row equilibration
solnum	Positive integer \| auto	auto	Solution number
study	Study tag	{First study}	Study to use with initmethod
symmetry	on \| off \| hermitian \| auto	auto	Symmetric matrices

The following values are valid for the out property:

Property/Value Pairs for the property out.
Property	expression	description
out	K	Stiffness matrix
	L	Load vector
	M	Constraint vector
	N	Constraint Jacobian
	D	Damping matrix
	E	Mass matrix
	NF	Constraint force Jacobian
	NP	Optimization constraint Jacobian (*)
	MP	Optimization constraint vector (*)
	MLB	Lower bound constraint vector (*)
	MUB	Upper bound constraint vector (*)
	Kc	Eliminated stiffness matrix
	Lc	Eliminated load vector
	Dc	Eliminated damping matrix
	Ec	Eliminated mass matrix
	Null	Constraint null-space basis
	Nullf	Constraint force null-space matrix
	ud	Particular solution ud
	uscale	Scale vector

(*) Requires the Optimization Module.

Note that the assembly of the eliminated matrices uses the current solution vector as scaling method. To get the unscaled eliminated system matrices, it is required to set the scaling method to 'none' in the variables step of the solver configuration node.

The load vector is assembled using the current solution available as linearization point unless the initmethod property is provided. In case of the presence of a solver step node in the solver sequence, the load vector correspond then to the residual of the problem.

The function mphmatrix does not solve the problem as the assembly is performed before the solver node in the solution sequence. You can specify the solution feature node after which to assemble the system matrices with the property extractafter. This is useful if you need to compute the solution before extracting the matrices or if you have a solution sequence using different solver sequences and you want to extract the matrices for a specific one.

The Advanced section in the COMSOL Multiphysics Reference Manual, describes the functionality corresponding to the properties complexfun, nullfun, and rowscale.

Use the property symmetric to assemble the model matrix system as symmetric/Hermitian, or you can use the automatic feature to find out (see Advanced in the COMSOL Multiphysics Reference Manual).

Example

Evaluate the system matrices of a stationary problem

model = mphopen('model_tutorial_llmatlab');

model.mesh('mesh1').autoMeshSize(8);

std = model.study.create('std1');

std.feature.create('stat', 'Stationary');

std.run;

Get the stationary matrix system, use the initial solution as linearization point:

str = mphmatrix(model,'sol1','out',{'K','L','M','N'},...

'initmethod','init');

Display the sparsity of the stiffness matrix and the constraint Jacobian and compute the total load applied in the matrix system:

subplot(2,1,1); spy(str.K);subplot(2,1,2);spy(str.N)