The Advanced node () is an attribute node that handles advanced settings for solver nodes, such as a Stationary Solver, Eigenvalue Solver, and Time-Dependent Solver. Also see About the Advanced Attribute Settings.

Use the Matrix symmetry list to control how the solver handles matrix symmetry of linear system matrices. Select:

Jacobian matrices requested by the solvers during solution can be stored in a sparse or a filled format, which you choose as Sparse or Filled, respectively, from the Matrix format list. In addition, you can choose a matrix-free format, which you choose as Free. The matrix-free representation allows evaluation of matrix-vector products without assembling the matrix. This can reduce the memory usage significantly for solver algorithms that only use the matrix to multiply a vector, specifically:

The default setting is Automatic. This setting chooses a sparse, filled, or matrix-free representation based on the equations being assembled and the solver used.

Even if variables are well scaled, equations can have very different scales. The Row equilibration check box is selected to balance the equations using row equilibration. Even when this check box is selected, row equilibration is not used in the following situations in order to preserve matrix symmetry:

Use the Null-space function list to select a method for the computation of matrices needed for constraint handling (see Elimination Constraint Handling). Select:

For the Automatic null-space function method, you can specify an Orthonormal block limit, which is used in the automatic choice between Orthonormal and Sparse handling (for elemental constraints). If an estimate of the complexity (the number of operations) needed to SVD factorize the largest constraint block exceeds this limit, the Sparse method is used. Else the Orthonormal method is used. The limit is 107 per default. To SVD factorize a block with this complexity is usually fast, so you might want to increase this limit for increased constraint handling stability.

You can store the last residual while solving and also in the solver output, if you want to access it using the residual operator during postprocessing. Storing the residual in the output increases the memory requirements for the simulations. From the Store last residual list, choose

The solver log contains information about the progress and convergence of the solvers (see The Log Window). From the Solver log list, choose one of the following formats:

For the time-dependent solvers, you can also specify an interval for the log sampling (in seconds) in the Log sampling (wall-clock) field when the Solver log list is set to Normal. The default is 0.005 s, which means that the log is updated at most every 0.005 s. Increasing the sampling interval can reduce the overhead associated with the log when solving problems with many small time steps. Set the value to 0 to make the log contain every time step regardless of their size.

When the Automatic rescaling of linear equations check box is selected, then under certain circumstances the scaling of the equations for the linear solvers can be changed to scales that are taken from the current solution. These circumstances are the following:

By default, the solver chooses the number of mesh elements that are processed together during the assembly process (the block size). Select the Assembly block size check box for manual specification of a block size for all null-space function methods except Automatic.

Select the Reuse sparsity pattern check box to store the sparsity patterns of the assembled matrices and try to reuse them for successive assembly processes within the same solution process. In many cases, the sparsity pattern of the system matrices does not change from one nonlinear iteration or time step to the others. Reusing the sparsity pattern from the previous iteration or step can then improve the solution performance at the cost of a usually small amount of memory. This functionality is enabled by default when using physics interfaces that can benefit from it. When active, the functionality can also detect whether the stored pattern cannot be used in the current assembly process (that is, when a “pattern mismatch” occurs) and reassemble it. If such a mismatch occurs, a message is added to the solver log. Pattern mismatches have no consequence on the solution process except for a small impact on the assembly performance during the current step or iteration due to the reassembling. Pattern mismatches can occur, for example, when solving a model with identity pairs and sliding meshes.

Select the Allow complex-valued output from functions with real input check box to control whether the solver treats such complex-valued output as an error or not.

The Stop when undefined mathematical operation is detected check box controls how the solver handles undefined mathematical operations such as division by zero.

Select the Check for undefined numerical values after each operation check box to make COMSOL Multiphysics check intermediate results for undefined numerical values (Inf or NaN) when numerical overflow occurs, for example. Selecting this option gives more accurate error messages when such undefined numerical values occur.

If desired, modify the drop tolerance in the Drop tolerance for local matrix contributions field (default value: 1·10−12). For semiconductor simulations, the default solver settings will use 0 as a value for the drop tolerance for local matrix contributions, which is a a drop tolerance that is better suited for such simulations.

Select the Manual control of reassembly check box to be able to override the solver mechanism that automatically detects which quantities need to be reassembled. This can be useful to improve efficiency in situations when the automatic mechanism is too sensitive and reassembles quantities that do not need to be reassembled.

If the Manual control of reassembly check box is selected, the Constant load is On by default.

The load (residual vector) is constant if the PDE and the Neumann boundary conditions are linear with time-independent coefficients and right-hand sides. For the discretized model, this means that the residual vector L depends linearly on U:

and that L0, K, D, and the mass matrix E are constant.

If you choose to turn Off the Constant load, it instructs the solver to perform a reassembly process for the computation of the residual vector (when Off) or not. However, even if it is off, you might still want to treat some of the matrices as constant. Manual control of reassembly of these quantities can be controlled with the available check boxes, which makes the assembly only occur once for the corresponding matrix.

If the Manual control of reassembly check box is selected, you can control reassembly of the constraint residual. By default the Constant constraint is On. The constraint is constant if the Dirichlet boundary conditions (constraints) are linear and time independent. For the discretized model, this means that the constraint residual M depends linearly on U (M = M0 − NU) and that M0 and N are constant. It is also assumed that the constraint Jacobian N is correct.

If you choose to turn Off the Constant constraint, it instructs the solver to perform a reassembly process for the computation of the constraint residual vector (when Off) or not. However, even if it is off, the constraint Jacobian might still be constant. To control the reassembly of this quantity, select the Constant constraint Jacobian check box if the Dirichlet boundary conditions are linear with time-independent coefficients (not right-hand side). For the discretized model this means that N is constant.