Combine Solutions
Use a Combine Solutions node () to combine two solutions using concatenation or summation or to remove solutions:
You can use concatenation to merge (concatenate) two time-dependent solutions that cover two disjunct time intervals so that it is possible to analyze and postprocess a combined solution over both time intervals. You can also concatenate two eigenfrequency or eigenvalue solutions.
You can use summation (a plain or weighted summation) to sum a number of eigensolutions, for example, for further analysis.
You can also remove solutions from a time-dependent solution, for example.
This node is also available in the solver configuration as a solver utility node. It then contains a General section, similar to the Combine Solutions Settings section below but with an additional Defined by study step list, which includes the Combine Solutions study steps and the User defined option for combining solutions at the solver level. By default, such Combine Solution nodes are generated from a corresponding Combine Solution node at the study level. At the solver level, there is also a Log section.
Parameter and variable definitions are copied from the source solution when the Combine Solutions node is computed. Use Update Solution (see Updating a Solution) to update parameters and variables to their current values.
The Settings window contains the following section.
Combine Solutions Settings
From the Solution operation list, choose Concatenation (the default), Summation, Weighted summation, General summation, or Remove solutions.
Concatenation
For a concatenation of two solutions, specify the two solutions from the First solution and Second solution lists. The lists contain all available solutions and Solution Store nodes (from this and other studies in the model), including Current, which is the default and is the output from the preceding study step.
The default for both solutions is Current, which is not a valid setting: the concatenation should be of two different time-dependent, parametric, or eigenvalue solutions, one of which may be the Current option. Stationary solutions cannot be combined.
From the Concatenation method list, choose First solution has precedence (the default) or Include all solutions. Use First solution has precedence to exclude solution numbers from the second solution whose parametric values can be found in the first solution. Use Include all solutions to include all solution numbers in the first solution and the second solution.
For a pure time-dependent solution with parameter size = 1, in the case of First solution has precedence:
For an overlapping interval, the First solution shadows the overlapped interval from the Second solution.
If the Add interpolated solution at intersection times checkbox is selected (see below), an interpolation is done for the Second solution at the interval boundaries of the First solution when these boundaries are also in the interval for the second solution.
Regarding concatenation of time-parametric solutions or multiparametric solutions with one continuous parameter: For solution numbers whose values of a discontinuous parameters in the First solution and Second solution lists are the same, the concatenation follows the rule for concatenation of continuous single-parametric solutions. For solution numbers whose values of discontinuous parameters in the First solution and Second solution lists are different, solutions from both the First solution and Second solution lists are kept in the concatenated solution.
The Add interpolated solution at intersection points for continuous parameter intervals checkbox is selected by default. This checkbox is only available when you have selected First solution has precedence, and it appears when the source solutions are parametric solutions with a continuous parameter that is not time. When selected, interpolation is done for the second solution at the intersection points for the continuous parameter. The results are always sorted for the continuous parameter values following the same order as it in the first solution.
The Add interpolated solution at intersection times checkbox is selected by default. This checkbox is only available when you have selected First solution has precedence, and it appears when the source solutions are time-dependent solutions. When selected, interpolation is done for the second solution at the intersection times. The results are always sorted for time following the same order as it in the first solution.
The Sort discontinuous single-parameter values checkbox is selected by default. This checkbox is available for both the First solution has precedence and Include all solutions methods. It appears when the source solutions are single-parametric solutions whose parameter is not continuous and is not an eigenvalue. When selected, the discontinuous parameter values are sorted in the combined solution.
If you concatenate solutions of an eigenvalue type, the following settings are available:
The Sort eigenvalues checkbox is selected by default. This checkbox is available for both the First solution has precedence and Include all solutions methods. It appears when the source solutions have only one parameter and are eigenvalue types of solutions like eigenvalue, eigenfrequency, or mode analysis. When selected, the relative parameter is sorted in the combined solution. The eigenvalues can be sorted in Ascending (the default) or Descending order depending on the Ordering setting. When the Sorting method is Predefined, you can choose to Sort primarily based on the Real part, Imaginary part, Real part magnitude, Imaginary part magnitude, or Absolute value. The same settings are available for the Sort secondly option, which is used to resolve conflicts. The defaults for eigenvalues are Real part for Sort primarily and Imaginary part magnitude for Sort secondly. For eigenfrequencies, the defaults are Imaginary part for Sort primarily and Imaginary part magnitude for Sort secondly. Also, the Sort based on transformed eigenvalues checkbox is selected by default to take and eigenvalue transformation into account when sorting. Alternatively, Manual can be chosen for the Sorting method and then an arbitrary number of (ordered) custom sorting priority expressions can be defined in the table that appears. In the Sorting priority expression column, add expressions for the sorting, in order of priority. Those expressions can be functions of the eigenvalue lambda or eigenfrequency freq. For example, you can specify an expression such as abs(freq-1) to sort according to the distance from a given shift (1 in this case). If desired, add some descriptive text in the Description column for the expressions. Select the Conjugate-pair consecutive sort checkbox to make complex-conjugate eigenpairs appear one after the other, regardless of the sorting rules.
You can also control the solution type and select the corresponding checkboxes manually before running the combine solution operation. From the Interpolation and sort list, choose Automatic or Manual. The default is Automatic, and it determines which of the checkboxes mentioned above that appear. For the Manual method, all applicable checkboxes are listed for each solution type. However, only relevant checkboxes are applied when computing the combined solution. From the Solution type list, choose Parametric, Time, or Eigenvalue. When the Solution type is Parametric, it means that the source solutions are parametric solutions with or without a continuous parameter. When the Solution type is Time, it means that the source solutions are time-dependent solutions, including time–parametric solutions. When the Solution type is Eigenvalue, it means that the source solutions are eigenvalue types of solutions, including eigenvalue–parametric solutions.
Summation and Weighted Summation
For a summation of solutions, from the Solution list, choose the source solution to sum up all solutions in that source solution. The default is Current, to use the current solution.
Additionally, for a weighted summation, choose a method for the weights from the Weights method list: One expression or List of expressions.
Choose One expression to use a single expression, in the Expression field, to define the weights for all solutions. The expression can be, for example, a constant value like 0.1 or a parameter-based scalar value like t. The result of the expression has to be a scalar. Weighted summation with the weights method set to One expression and Expression being 1 is the same as Summation.
Choose List of expressions to define a list of expressions in the table below. The Indices column contains the solution numbers whose solutions are to be summed up. Solution whose solution numbers are not shown in the table will not be summed up. The expressions in the List of expressions column define how the weights are calculated. Different solution numbers can have their own weight expressions. Each expression should result in a scalar number. The status of the checkboxes in the Active column determines whether the corresponding solution number is taken into account in the summation or not.
If you only want to use the combined solution for a weighted summation, select the Clear source solution checkbox.
General Summation
Use this option to sum up all solutions in the source solution based on Component expressions, which are used to compute the corresponding DOFs in the solution vectors. You can use different expressions for different component names in the table that appears. For example, by default, the Component expressions are the component names themselves, in which case the general summation produces the same result as Summation and Weighted summation with weight 1. The Component expressions can also be the function of the component names like (comp1.u)^2 or abs(comp1.u), for which the general summation sum up the squares of all solutions or the absolute value of all solutions, respectively.
From the Solution list, choose the source solution of the general summation. The default is Current, to use the current solution.
The General summation option is only available for Combine Solution nodes that are added under a Solution node.
Remove Solutions
If you choose Remove solutions, you can remove some solutions (such as some eigenmodes, parametric solutions, or time steps) from the input solution. When using the Remove Solutions operation, from the Exclude or include list, choose Exclude (the default) or Include to use the criteria for choosing solutions as the ones to exclude or include.
From the Exclude method or Include method list, choose Explicit (the default) or Implicit to use an explicit choice of solutions or an implicit choice using Boolean expressions for the solutions to exclude or include.
For Explicit, choose All, From list, or Manual from the Selection list. For From list, choose solutions to exclude or include from the list. For Manual, enter solutions as indices (integers) in the Index field.
For Implicit, enter a Boolean expression in the Exclude if or Include if field. All solutions for which the expression evaluates to true are excluded or included. For example, if the source solution is a time-dependent solution, the Exclude if or Include if field can have an expression like t>0.25, meaning that only solutions whose parameter t is larger than 0.25 will be included or excluded.
If you only want to use the combined solution (a version of the input solution with some solutions removed), select the Clear source solution checkbox.
See Axisymmetric Transient Heat Transfer: Application Library path COMSOL_Multiphysics/Heat_Transfer/heat_transient_axi.