— Class: <COEFFICIENT>

The coefficient class.

Direct slots:

• DIMENSION: The dimension of the cell on which this coefficient is active. The value T means that it is active on all cells lying on the patch.
• DEMANDS: A list indicating which information the evaluation function needs. Possible choices depend on problem and discretization, e.g. :local, :global, :fe, :cell are possible choices. One element can also be a list starting with the keyword :fe-parameters and followed by symbols indicating names of finite element functions on the discretization blackboard.
• EVAL: The evaluation funtion. It accepts a list of keyword parameters which should correspond to the list in DEMANDS.
• RESIDUAL: T means evaluation for computing the residual.
• JACOBIAN: T means evaluation for computing the Jacobian.

— Class: <DOMAIN-PROBLEM>

An instance of this class describes a problem posed on the domain domain. The slot coefficients contains a table mapping domain patches to property lists of the form (identifier1 coefficient1 identifier2 coefficient2 ...). Here identifiers are special symbols and the coefficients are objects of type <coefficient>. When the problem instance is initialized this table is usually set up by calling the function patch->coefficients which has to be provided as a key argument. The slot multiplicity can be chosen as a positive integer n if the problem is posed with n different right hand sides simultaneously.

Note also that for nonlinear problems, where the coefficients depend on the solution, an approximate solution can be found as a property of the problem.

Superclasses: <PROBLEM>

Direct slots:

• DOMAIN: NIL
• COEFFICIENTS: Hash table which maps domain patches to coefficients.
• MULTIPLICITY: NIL

— Class: <EVP-MIXIN>

A mixin for eigenvalue problems.

Direct slots:

• LAMBDA: The multiplier for the mass matrix, usually equal to the eigenvalue.
• MU: The multiplier for the system matrix.

— Class: <EVP>

Standard class for discrete eigenvalue problems.

Superclasses: <EVP-MIXIN> <NONLINEAR-PROBLEM>

— Class: <INTERPOLATION-PROBLEM>

Interpolation problem on a domain. The function which is to be interpolated is given as a coefficient with key FUNCTION in the coefficient list.

Superclasses: <DOMAIN-PROBLEM>

— Class: <LS-EVP>

Generalized eigenvalue problem for matrices.

Superclasses: <EVP>

Direct slots:

• A: (Energy) matrix A.
• B: (Mass) matrix B.

— Class: <LSE>

Standard form of a linear system of equations.

Superclasses: <PROBLEM>

Direct slots:

• MATRIX: NIL
• RHS: NIL

— Class: <NLSE>

Class for nonlinear system of equations.

Superclasses: <NONLINEAR-PROBLEM>

— Class: <NONLINEAR-PROBLEM>

Class for nonlinear problems. The linearization contains a function returning a linear problem.

Superclasses: <PROBLEM>

Direct slots:

• LINEARIZATION: A function linearizing the problem.
• INITIAL-GUESS: An initial guess for a solution.

— Class: <PDE-PROBLEM>

Base-class for a pde-problem.

Superclasses: <DOMAIN-PROBLEM>

— Class: <PROBLEM>

Base class for all problems.

Superclasses: PROPERTY-MIXIN

— Class: <SOLVER>

The base class of linear, nonlinear and whatever iterative solvers.

Direct slots:

• OUTPUT: NIL

— Class: <TIME-DEPENDENT-PROBLEM>

A mixin which should be used together with a <PDE-PROBLEM> in a call to MAKE-PROGRAMMATIC-INSTANCE.

— Function: ADD-FE-PARAMETERS-DEMAND DEMANDS NEW-PARAS

Adds a list of fe-functions to the demands.

— Function: BOUNDARY-COEFFICIENT-P PROBLEM COEFF

Tests, if coeff is a boundary coefficient of problem.

— Function: BOUNDARY-COEFFICIENTS PROBLEM

Returns a list of possible boundary coefficients for problem.

— Function: COEFFICIENT-P PROBLEM COEFF

Test if coeff is a coefficient of problem.

— Function: COEFFICIENTS-OF-CELL CELL MESH MSP

An accessor for the coefficients of problem valid for cell.

— Function: COEFFICIENTS-OF-PATCH PATCH PROBLEM

An accessor for the coefficients of patch for problem.

— Function: CONSTANT-COEFFICIENT VALUE &REST OTHER-VALUES

Returns a coefficient which takes the given value. Several values can be passed which is needed, for example, for returning also the type of a boundary condition.

— Function: CONSTRAINT-COEFFICIENT COMPONENTS MULTIPLICITY

Returns a coefficient function which sets Dirichlet zero boundary conditions for all components of a PDE system.

— Function: DUAL-PROBLEM PROBLEM CELL->RHS

Returns the dual problem for problem with the right-hand side given by functional. The solution of this problem measures the sensitivity of functional applied to the solution of problem with respect to errors in the solution.

— Function: ENERGY EVP X

Evaluates the energy bilinear form for a generalized eigenvalue problem.

— Function: ENSURE-COEFFICIENT OBJ

Returns obj if it is a coefficient, converts obj into a coefficient depending on the space variable if obj is a function; otherwise, obj is made into a constant coefficient.

— Function: ENSURE-RESIDUAL LSE BLACKBOARD

Ensures that the field :RESIDUAL is computed and that the flag :RESIDUAL-P is set on the blackboard.

— Function: ENSURE-SOLUTION NLPB BLACKBOARD

Ensures that the field :SOLUTION is set on the blackboard.

— Function: FILTER-APPLICABLE-COEFFICIENTS COEFFS CELL PATCH &KEY (CONSTRAINTS T)

Filters out the applicable coefficients for the respective cell with the given patch.

— Function: F[U]->COEFFICIENT FUNC

The function argument func is transformed into a coefficient depending on the solution.

— Function: F[XU]->COEFFICIENT FUNC

The function argument func is transformed into a coefficient depending on position and solution.

— Function: F[X]->COEFFICIENT FUNC

The function argument func is transformed into a coefficient depending on global coordinates.

— Function: GET-COEFFICIENT COEFFS NAME

Get coefficient name from the list coeffs.

— Function: GET-PROPERTY OBJECT PROPERTY

Gets property for object.

— Function: INTERIOR-COEFFICIENT-P PROBLEM COEFF

Tests, if coeff is an interior coefficient of problem.

— Function: INTERIOR-COEFFICIENTS PROBLEM

Returns a list of possible interior coefficients for problem.

— Function: LINEAR-P PROBLEM

Predicate determining if a problem is linear or nonlinear.

— Function: LINEARIZE PROBLEM SOLUTION

Linearize the nonlinear problem PROBLEM at the point SOLUTION. The result should be a linear problem.

— Function: LSE &REST ARGS

Constructs a standard LSE.

— Function: MAP-COEFFICIENTS FUNC COEFFS

Maps a given coefficient list coeffs into a new coefficient list. func takes coefficient name and coefficient and returns two values for new coefficient name and coefficient. If the first value returned is NIL, this coefficient is not collected.

— Function: MASS EVP X

Evaluates the mass bilinear form for a generalized eigenvalue problem.

— Function: MULTIPLICITY <ANSATZ-SPACE>

We allow multiple vectors, for solving linear problems in parallel.

— Function: NLSE &REST ARGS

Constructs a standard NLSE.

— Function: NR-OF-COMPONENTS MSFE

Returns the number of components for problem.

— Function: REQUIRED-FE-FUNCTIONS COEFFS

Returns a list of finite element functions required by the coefficients in the property list coeffs.

— Function: SELECT-LINEAR-SOLVER PROBLEM BLACKBOARD

Selects a linear solver for OBJECT. OBJECT is usually a matrix or a linear problem with certain characteristics.

— Function: SELECT-SOLVER PROBLEM BLACKBOARD

Selects a solver for OBJECT. OBJECT is usually a problem with certain characteristics.

— Function: SELF-ADJOINT-P PROBLEM

Returns two values. The first says if problem is self-adjoint, the second says if that value has really been checked.

— Function: SOLVE BLACKBOARD &OPTIONAL DUMMY

Solve a problem specified on the blackboard. Returns a modified blackboard. The returned blackboard is guaranteed to contain at least the fields :solution and :status. :status is one of the values :success or :failure.

SOLVE can also be called as (SOLVE blackboard) and will then try to figure out a suitable solver itself.

— Function: STATIONARY-PROBLEM-CLASS TDP

Finds the stationary pde problem for the time-dependent problem TDP.

— Function: ZERO-CONSTRAINTS PROBLEM

Returns a coefficient function which constrains all system components to zero.