Example 1 with ConstructedSolutionTemplate
use of cbit.vcell.numericstest.ConstructedSolutionTemplate in project vcell by virtualcell.
the class SolutionTemplateTableModel method setConstructedSolutionTemplate.
/**
* Sets the constructedSolutionTemplate property (cbit.vcell.numericstest.ConstructedSolutionTemplate) value.
* @param constructedSolutionTemplate The new value for the property.
* @see #getConstructedSolutionTemplate
*/
public void setConstructedSolutionTemplate(cbit.vcell.numericstest.ConstructedSolutionTemplate constructedSolutionTemplate) {
ConstructedSolutionTemplate oldValue = fieldConstructedSolutionTemplate;
fieldConstructedSolutionTemplate = constructedSolutionTemplate;
firePropertyChange("constructedSolutionTemplate", oldValue, constructedSolutionTemplate);
fireTableDataChanged();
}
Also used :
ConstructedSolutionTemplate(cbit.vcell.numericstest.ConstructedSolutionTemplate)
Example 2 with ConstructedSolutionTemplate
use of cbit.vcell.numericstest.ConstructedSolutionTemplate in project vcell by virtualcell.
the class MathTestingUtilities method constructExactMath.
/**
* constructExactMath()
*
* take an equation of the form:
*
* d A
* --- = F(A,t)
* d t
*
* and create a new equation with a known exact solution 'A_exact' by adding a forcing function R(t)
*
* d A
* --- = F(A,t) + R(t)
* d t
*
* where:
*
* d A_exact
* R(t) = --------- - F(A_exact,t)
* d t
*
* solving for R(t) is done analytically.
*
* Creation date: (1/21/2003 10:47:54 AM)
* @return cbit.vcell.math.MathDescription
* @param mathDesc cbit.vcell.math.MathDescription
*/
public static MathDescription constructExactMath(MathDescription mathDesc, java.util.Random random, ConstructedSolutionTemplate constructedSolutionTemplate) throws ExpressionException, MathException, MappingException {
if (mathDesc.hasFastSystems()) {
throw new RuntimeException("SolverTest.constructExactMath() suppport for fastSystems not yet implemented.");
}
MathDescription exactMath = null;
try {
exactMath = (MathDescription) BeanUtils.cloneSerializable(mathDesc);
exactMath.setDescription("constructed exact solution from MathDescription (" + mathDesc.getName() + ")");
exactMath.setName("exact from " + mathDesc.getName());
} catch (Throwable e) {
e.printStackTrace(System.out);
throw new RuntimeException("error cloning MathDescription: " + e.getMessage());
}
//
// preload the VariableHash with existing Variables (and Constants,Functions,etc) and then sort all at once.
//
VariableHash varHash = new VariableHash();
Enumeration<Variable> enumVar = exactMath.getVariables();
while (enumVar.hasMoreElements()) {
varHash.addVariable(enumVar.nextElement());
}
java.util.Enumeration<SubDomain> subDomainEnum = exactMath.getSubDomains();
while (subDomainEnum.hasMoreElements()) {
SubDomain subDomain = subDomainEnum.nextElement();
Domain domain = new Domain(subDomain);
java.util.Enumeration<Equation> equationEnum = subDomain.getEquations();
if (subDomain instanceof MembraneSubDomain) {
MembraneSubDomain memSubDomain = (MembraneSubDomain) subDomain;
AnalyticSubVolume insideAnalyticSubVolume = (AnalyticSubVolume) exactMath.getGeometry().getGeometrySpec().getSubVolume(memSubDomain.getInsideCompartment().getName());
Function[] outwardNormalFunctions = getOutwardNormal(insideAnalyticSubVolume.getExpression(), "_" + insideAnalyticSubVolume.getName());
for (int i = 0; i < outwardNormalFunctions.length; i++) {
varHash.addVariable(outwardNormalFunctions[i]);
}
}
while (equationEnum.hasMoreElements()) {
Equation equation = equationEnum.nextElement();
if (equation.getExactSolution() != null) {
throw new RuntimeException("exact solution already exists");
}
Enumeration<Constant> origMathConstants = mathDesc.getConstants();
if (equation instanceof OdeEquation) {
OdeEquation odeEquation = (OdeEquation) equation;
Expression substitutedRateExp = substituteWithExactSolution(odeEquation.getRateExpression(), (CompartmentSubDomain) subDomain, exactMath);
SolutionTemplate solutionTemplate = constructedSolutionTemplate.getSolutionTemplate(equation.getVariable().getName(), subDomain.getName());
String varName = odeEquation.getVariable().getName();
String initName = null;
while (origMathConstants.hasMoreElements()) {
Constant constant = origMathConstants.nextElement();
if (constant.getName().startsWith(varName + "_" + subDomain.getName() + DiffEquMathMapping.MATH_FUNC_SUFFIX_SPECIES_INIT_CONC_UNIT_PREFIX)) {
initName = constant.getName();
}
}
String exactName = varName + "_" + subDomain.getName() + "_exact";
String errorName = varName + "_" + subDomain.getName() + "_error";
String origRateName = "_" + varName + "_" + subDomain.getName() + "_origRate";
String substitutedRateName = "_" + varName + "_" + subDomain.getName() + "_substitutedRate";
String exactTimeDerivativeName = "_" + varName + "_" + subDomain.getName() + "_exact_dt";
Expression exactExp = solutionTemplate.getTemplateExpression();
Expression errorExp = new Expression(exactName + " - " + varName);
Expression origRateExp = new Expression(odeEquation.getRateExpression());
Expression exactTimeDerivativeExp = exactExp.differentiate("t").flatten();
Expression newRate = new Expression(origRateName + " - " + substitutedRateName + " + " + exactTimeDerivativeName);
Constant[] constants = solutionTemplate.getConstants();
for (int i = 0; i < constants.length; i++) {
varHash.addVariable(constants[i]);
}
Expression initExp = new Expression(exactExp);
initExp.substituteInPlace(new Expression("t"), new Expression(0.0));
varHash.addVariable(new Function(initName, initExp.flatten(), domain));
varHash.addVariable(new Function(exactName, exactExp, domain));
varHash.addVariable(new Function(errorName, errorExp, domain));
varHash.addVariable(new Function(exactTimeDerivativeName, exactTimeDerivativeExp, domain));
varHash.addVariable(new Function(origRateName, origRateExp, domain));
varHash.addVariable(new Function(substitutedRateName, substitutedRateExp, domain));
odeEquation.setRateExpression(newRate);
odeEquation.setInitialExpression(new Expression(initName));
odeEquation.setExactSolution(new Expression(exactName));
} else if (equation instanceof PdeEquation) {
PdeEquation pdeEquation = (PdeEquation) equation;
Expression substitutedRateExp = substituteWithExactSolution(pdeEquation.getRateExpression(), (CompartmentSubDomain) subDomain, exactMath);
SolutionTemplate solutionTemplate = constructedSolutionTemplate.getSolutionTemplate(equation.getVariable().getName(), subDomain.getName());
String varName = pdeEquation.getVariable().getName();
String initName = null;
while (origMathConstants.hasMoreElements()) {
Constant constant = origMathConstants.nextElement();
if (constant.getName().startsWith(varName + "_" + subDomain.getName() + DiffEquMathMapping.MATH_FUNC_SUFFIX_SPECIES_INIT_CONC_UNIT_PREFIX)) {
initName = constant.getName();
}
}
String diffusionRateName = "_" + varName + "_" + subDomain.getName() + "_diffusionRate";
String exactName = varName + "_" + subDomain.getName() + "_exact";
String errorName = varName + "_" + subDomain.getName() + "_error";
String origRateName = "_" + varName + "_" + subDomain.getName() + "_origRate";
String substitutedRateName = "_" + varName + "_" + subDomain.getName() + "_substitutedRate";
String exactTimeDerivativeName = "_" + varName + "_" + subDomain.getName() + "_exact_dt";
String exactDxName = "_" + varName + "_" + subDomain.getName() + "_exact_dx";
String exactDyName = "_" + varName + "_" + subDomain.getName() + "_exact_dy";
String exactDzName = "_" + varName + "_" + subDomain.getName() + "_exact_dz";
String exactDx2Name = "_" + varName + "_" + subDomain.getName() + "_exact_dx2";
String exactDy2Name = "_" + varName + "_" + subDomain.getName() + "_exact_dy2";
String exactDz2Name = "_" + varName + "_" + subDomain.getName() + "_exact_dz2";
String exactLaplacianName = "_" + varName + "_" + subDomain.getName() + "_exact_laplacian";
Expression exactExp = solutionTemplate.getTemplateExpression();
Expression errorExp = new Expression(exactName + " - " + varName);
Expression origRateExp = new Expression(pdeEquation.getRateExpression());
Expression initExp = new Expression(exactExp);
initExp.substituteInPlace(new Expression("t"), new Expression(0.0));
initExp = initExp.flatten();
Expression exactTimeDerivativeExp = exactExp.differentiate("t").flatten();
Expression exactDxExp = exactExp.differentiate("x").flatten();
Expression exactDx2Exp = exactDxExp.differentiate("x").flatten();
Expression exactDyExp = exactExp.differentiate("y").flatten();
Expression exactDy2Exp = exactDxExp.differentiate("y").flatten();
Expression exactDzExp = exactExp.differentiate("z").flatten();
Expression exactDz2Exp = exactDxExp.differentiate("z").flatten();
Expression exactLaplacianExp = Expression.add(Expression.add(exactDx2Exp, exactDy2Exp), exactDz2Exp).flatten();
Expression newRate = new Expression(origRateName + " - " + substitutedRateName + " - ((" + diffusionRateName + ")*" + exactLaplacianName + ")" + " + " + exactTimeDerivativeName);
Constant[] constants = solutionTemplate.getConstants();
for (int i = 0; i < constants.length; i++) {
varHash.addVariable(constants[i]);
}
varHash.addVariable(new Function(initName, initExp, domain));
varHash.addVariable(new Function(diffusionRateName, new Expression(pdeEquation.getDiffusionExpression()), domain));
varHash.addVariable(new Function(exactName, exactExp, domain));
varHash.addVariable(new Function(errorName, errorExp, domain));
varHash.addVariable(new Function(exactTimeDerivativeName, exactTimeDerivativeExp, domain));
varHash.addVariable(new Function(origRateName, origRateExp, domain));
varHash.addVariable(new Function(substitutedRateName, substitutedRateExp, domain));
varHash.addVariable(new Function(exactDxName, exactDxExp, domain));
varHash.addVariable(new Function(exactDyName, exactDyExp, domain));
varHash.addVariable(new Function(exactDzName, exactDzExp, domain));
varHash.addVariable(new Function(exactDx2Name, exactDx2Exp, domain));
varHash.addVariable(new Function(exactDy2Name, exactDy2Exp, domain));
varHash.addVariable(new Function(exactDz2Name, exactDz2Exp, domain));
varHash.addVariable(new Function(exactLaplacianName, exactLaplacianExp, domain));
pdeEquation.setRateExpression(newRate);
pdeEquation.setInitialExpression(new Expression(initName));
pdeEquation.setDiffusionExpression(new Expression(diffusionRateName));
pdeEquation.setExactSolution(new Expression(exactName));
CompartmentSubDomain compartmentSubDomain = (CompartmentSubDomain) subDomain;
if (compartmentSubDomain.getBoundaryConditionXm().isDIRICHLET()) {
Expression origExp = pdeEquation.getBoundaryXm();
if (origExp != null) {
Expression substitutedExp = substituteWithExactSolution(origExp, compartmentSubDomain, exactMath);
pdeEquation.setBoundaryXm(new Expression(origExp + "-" + substitutedExp + "+" + exactExp));
} else {
pdeEquation.setBoundaryXm(exactExp);
}
} else if (compartmentSubDomain.getBoundaryConditionXm().isNEUMANN()) {
Expression origExp = pdeEquation.getBoundaryXm();
if (origExp != null) {
Expression substitutedExp = substituteWithExactSolution(origExp, compartmentSubDomain, exactMath);
pdeEquation.setBoundaryXm(new Expression(origExp + "-" + substitutedExp + "-" + diffusionRateName + "*" + exactDxName));
} else {
pdeEquation.setBoundaryXm(new Expression("-" + diffusionRateName + "*" + exactDxName));
}
} else {
throw new RuntimeException("unsupported boundary condition type " + compartmentSubDomain.getBoundaryConditionXm());
}
if (compartmentSubDomain.getBoundaryConditionXp().isDIRICHLET()) {
Expression origExp = pdeEquation.getBoundaryXp();
if (origExp != null) {
Expression substitutedExp = substituteWithExactSolution(origExp, compartmentSubDomain, exactMath);
pdeEquation.setBoundaryXp(new Expression(origExp + "-" + substitutedExp + "+" + exactExp));
} else {
pdeEquation.setBoundaryXp(exactExp);
}
} else if (compartmentSubDomain.getBoundaryConditionXp().isNEUMANN()) {
Expression origExp = pdeEquation.getBoundaryXp();
if (origExp != null) {
Expression substitutedExp = substituteWithExactSolution(origExp, compartmentSubDomain, exactMath);
pdeEquation.setBoundaryXp(new Expression(origExp + "-" + substitutedExp + "+" + diffusionRateName + "*" + exactDxName));
} else {
pdeEquation.setBoundaryXp(new Expression(diffusionRateName + "*" + exactDxName));
}
} else {
throw new RuntimeException("unsupported boundary condition type " + compartmentSubDomain.getBoundaryConditionXp());
}
if (compartmentSubDomain.getBoundaryConditionYm().isDIRICHLET()) {
Expression origExp = pdeEquation.getBoundaryYm();
if (origExp != null) {
Expression substitutedExp = substituteWithExactSolution(origExp, compartmentSubDomain, exactMath);
pdeEquation.setBoundaryYm(new Expression(origExp + "-" + substitutedExp + "+" + exactExp));
} else {
pdeEquation.setBoundaryYm(exactExp);
}
} else if (compartmentSubDomain.getBoundaryConditionYm().isNEUMANN()) {
Expression origExp = pdeEquation.getBoundaryYm();
if (origExp != null) {
Expression substitutedExp = substituteWithExactSolution(origExp, compartmentSubDomain, exactMath);
pdeEquation.setBoundaryYm(new Expression(origExp + "-" + substitutedExp + "-" + diffusionRateName + "*" + exactDyName));
} else {
pdeEquation.setBoundaryYm(new Expression("-" + diffusionRateName + "*" + exactDyName));
}
} else {
throw new RuntimeException("unsupported boundary condition type " + compartmentSubDomain.getBoundaryConditionYm());
}
if (compartmentSubDomain.getBoundaryConditionYp().isDIRICHLET()) {
Expression origExp = pdeEquation.getBoundaryYp();
if (origExp != null) {
Expression substitutedExp = substituteWithExactSolution(origExp, compartmentSubDomain, exactMath);
pdeEquation.setBoundaryYp(new Expression(origExp + "-" + substitutedExp + "+" + exactExp));
} else {
pdeEquation.setBoundaryYp(exactExp);
}
} else if (compartmentSubDomain.getBoundaryConditionYp().isNEUMANN()) {
Expression origExp = pdeEquation.getBoundaryYp();
if (origExp != null) {
Expression substitutedExp = substituteWithExactSolution(origExp, compartmentSubDomain, exactMath);
pdeEquation.setBoundaryYp(new Expression(origExp + "-" + substitutedExp + "+" + diffusionRateName + "*" + exactDyName));
} else {
pdeEquation.setBoundaryYp(new Expression(diffusionRateName + "*" + exactDyName));
}
} else {
throw new RuntimeException("unsupported boundary condition type " + compartmentSubDomain.getBoundaryConditionYp());
}
if (compartmentSubDomain.getBoundaryConditionZm().isDIRICHLET()) {
Expression origExp = pdeEquation.getBoundaryZm();
if (origExp != null) {
Expression substitutedExp = substituteWithExactSolution(origExp, compartmentSubDomain, exactMath);
pdeEquation.setBoundaryZm(new Expression(origExp + "-" + substitutedExp + "+" + exactExp));
} else {
pdeEquation.setBoundaryZm(exactExp);
}
} else if (compartmentSubDomain.getBoundaryConditionZm().isNEUMANN()) {
Expression origExp = pdeEquation.getBoundaryZm();
if (origExp != null) {
Expression substitutedExp = substituteWithExactSolution(origExp, compartmentSubDomain, exactMath);
pdeEquation.setBoundaryZm(new Expression(origExp + "-" + substitutedExp + "-" + diffusionRateName + "*" + exactDzName));
} else {
pdeEquation.setBoundaryZm(new Expression("-" + diffusionRateName + "*" + exactDzName));
}
} else {
throw new RuntimeException("unsupported boundary condition type " + compartmentSubDomain.getBoundaryConditionXm());
}
if (compartmentSubDomain.getBoundaryConditionZp().isDIRICHLET()) {
Expression origExp = pdeEquation.getBoundaryZp();
if (origExp != null) {
Expression substitutedExp = substituteWithExactSolution(origExp, compartmentSubDomain, exactMath);
pdeEquation.setBoundaryZp(new Expression(origExp + "-" + substitutedExp + "+" + exactExp));
} else {
pdeEquation.setBoundaryZp(exactExp);
}
} else if (compartmentSubDomain.getBoundaryConditionZp().isNEUMANN()) {
Expression origExp = pdeEquation.getBoundaryZp();
if (origExp != null) {
Expression substitutedExp = substituteWithExactSolution(origExp, compartmentSubDomain, exactMath);
pdeEquation.setBoundaryZp(new Expression(origExp + "-" + substitutedExp + "+" + diffusionRateName + "*" + exactDzName));
} else {
pdeEquation.setBoundaryZp(new Expression(diffusionRateName + "*" + exactDzName));
}
} else {
throw new RuntimeException("unsupported boundary condition type " + compartmentSubDomain.getBoundaryConditionZp());
}
} else {
throw new RuntimeException("SolverTest.constructedExactMath(): equation type " + equation.getClass().getName() + " not yet implemented");
}
}
if (subDomain instanceof MembraneSubDomain) {
MembraneSubDomain membraneSubDomain = (MembraneSubDomain) subDomain;
Enumeration<JumpCondition> enumJumpConditions = membraneSubDomain.getJumpConditions();
while (enumJumpConditions.hasMoreElements()) {
JumpCondition jumpCondition = enumJumpConditions.nextElement();
Expression origInfluxExp = jumpCondition.getInFluxExpression();
Expression origOutfluxExp = jumpCondition.getOutFluxExpression();
Expression substitutedInfluxExp = substituteWithExactSolution(origInfluxExp, membraneSubDomain, exactMath);
Expression substitutedOutfluxExp = substituteWithExactSolution(origOutfluxExp, membraneSubDomain, exactMath);
String varName = jumpCondition.getVariable().getName();
String origInfluxName = "_" + varName + "_" + subDomain.getName() + "_origInflux";
String origOutfluxName = "_" + varName + "_" + subDomain.getName() + "_origOutflux";
String substitutedInfluxName = "_" + varName + "_" + subDomain.getName() + "_substitutedInflux";
String substitutedOutfluxName = "_" + varName + "_" + subDomain.getName() + "_substitutedOutflux";
String diffusionRateInsideName = "_" + varName + "_" + membraneSubDomain.getInsideCompartment().getName() + "_diffusionRate";
String diffusionRateOutsideName = "_" + varName + "_" + membraneSubDomain.getOutsideCompartment().getName() + "_diffusionRate";
String exactInsideDxName = "_" + varName + "_" + membraneSubDomain.getInsideCompartment().getName() + "_exact_dx";
String exactInsideDyName = "_" + varName + "_" + membraneSubDomain.getInsideCompartment().getName() + "_exact_dy";
String exactInsideDzName = "_" + varName + "_" + membraneSubDomain.getInsideCompartment().getName() + "_exact_dz";
String exactOutsideDxName = "_" + varName + "_" + membraneSubDomain.getOutsideCompartment().getName() + "_exact_dx";
String exactOutsideDyName = "_" + varName + "_" + membraneSubDomain.getOutsideCompartment().getName() + "_exact_dy";
String exactOutsideDzName = "_" + varName + "_" + membraneSubDomain.getOutsideCompartment().getName() + "_exact_dz";
String outwardNormalXName = "_" + membraneSubDomain.getInsideCompartment().getName() + "_Nx";
String outwardNormalYName = "_" + membraneSubDomain.getInsideCompartment().getName() + "_Ny";
String outwardNormalZName = "_" + membraneSubDomain.getInsideCompartment().getName() + "_Nz";
String exactInfluxName = "_" + varName + "_" + membraneSubDomain.getName() + "_exactInflux";
String exactOutfluxName = "_" + varName + "_" + membraneSubDomain.getName() + "_exactOutflux";
Expression exactInfluxExp = new Expression(diffusionRateInsideName + " * (" + outwardNormalXName + "*" + exactInsideDxName + " + " + outwardNormalYName + "*" + exactInsideDyName + " + " + outwardNormalZName + "*" + exactInsideDzName + ")");
Expression exactOutfluxExp = new Expression("-" + diffusionRateOutsideName + " * (" + outwardNormalXName + "*" + exactOutsideDxName + " + " + outwardNormalYName + "*" + exactOutsideDyName + " + " + outwardNormalZName + "*" + exactOutsideDzName + ")");
Expression newInfluxExp = new Expression(origInfluxName + " - " + substitutedInfluxName + " + " + exactInfluxName);
Expression newOutfluxExp = new Expression(origOutfluxName + " - " + substitutedOutfluxName + " + " + exactOutfluxName);
varHash.addVariable(new Function(origInfluxName, origInfluxExp, domain));
varHash.addVariable(new Function(origOutfluxName, origOutfluxExp, domain));
varHash.addVariable(new Function(exactInfluxName, exactInfluxExp, domain));
varHash.addVariable(new Function(exactOutfluxName, exactOutfluxExp, domain));
varHash.addVariable(new Function(substitutedInfluxName, substitutedInfluxExp, domain));
varHash.addVariable(new Function(substitutedOutfluxName, substitutedOutfluxExp, domain));
jumpCondition.setInFlux(newInfluxExp);
jumpCondition.setOutFlux(newOutfluxExp);
}
}
}
exactMath.setAllVariables(varHash.getAlphabeticallyOrderedVariables());
if (!exactMath.isValid()) {
throw new RuntimeException("generated Math is not valid: " + exactMath.getWarning());
}
return exactMath;
}
Also used :
JumpCondition(cbit.vcell.math.JumpCondition)
MembraneSubDomain(cbit.vcell.math.MembraneSubDomain)
MembraneRegionVariable(cbit.vcell.math.MembraneRegionVariable)
InsideVariable(cbit.vcell.math.InsideVariable)
SensVariable(cbit.vcell.solver.ode.SensVariable)
FilamentVariable(cbit.vcell.math.FilamentVariable)
VolVariable(cbit.vcell.math.VolVariable)
VolumeRegionVariable(cbit.vcell.math.VolumeRegionVariable)
ReservedVariable(cbit.vcell.math.ReservedVariable)
MemVariable(cbit.vcell.math.MemVariable)
OutsideVariable(cbit.vcell.math.OutsideVariable)
FilamentRegionVariable(cbit.vcell.math.FilamentRegionVariable)
Variable(cbit.vcell.math.Variable)
MathDescription(cbit.vcell.math.MathDescription)
VariableHash(cbit.vcell.math.VariableHash)
Constant(cbit.vcell.math.Constant)
CompartmentSubDomain(cbit.vcell.math.CompartmentSubDomain)
SubDomain(cbit.vcell.math.SubDomain)
MembraneSubDomain(cbit.vcell.math.MembraneSubDomain)
PdeEquation(cbit.vcell.math.PdeEquation)
Function(cbit.vcell.math.Function)
OdeEquation(cbit.vcell.math.OdeEquation)
PdeEquation(cbit.vcell.math.PdeEquation)
Equation(cbit.vcell.math.Equation)
SolutionTemplate(cbit.vcell.numericstest.SolutionTemplate)
ConstructedSolutionTemplate(cbit.vcell.numericstest.ConstructedSolutionTemplate)
OdeEquation(cbit.vcell.math.OdeEquation)
Expression(cbit.vcell.parser.Expression)
CompartmentSubDomain(cbit.vcell.math.CompartmentSubDomain)
CompartmentSubDomain(cbit.vcell.math.CompartmentSubDomain)
SubDomain(cbit.vcell.math.SubDomain)
Domain(cbit.vcell.math.Variable.Domain)
MembraneSubDomain(cbit.vcell.math.MembraneSubDomain)
AnalyticSubVolume(cbit.vcell.geometry.AnalyticSubVolume)
Aggregations
ConstructedSolutionTemplate (cbit.vcell.numericstest.ConstructedSolutionTemplate)2
AnalyticSubVolume (cbit.vcell.geometry.AnalyticSubVolume)1
CompartmentSubDomain (cbit.vcell.math.CompartmentSubDomain)1
Constant (cbit.vcell.math.Constant)1
Equation (cbit.vcell.math.Equation)1
FilamentRegionVariable (cbit.vcell.math.FilamentRegionVariable)1
FilamentVariable (cbit.vcell.math.FilamentVariable)1
Function (cbit.vcell.math.Function)1
InsideVariable (cbit.vcell.math.InsideVariable)1
JumpCondition (cbit.vcell.math.JumpCondition)1
MathDescription (cbit.vcell.math.MathDescription)1
MemVariable (cbit.vcell.math.MemVariable)1
MembraneRegionVariable (cbit.vcell.math.MembraneRegionVariable)1
MembraneSubDomain (cbit.vcell.math.MembraneSubDomain)1
OdeEquation (cbit.vcell.math.OdeEquation)1
OutsideVariable (cbit.vcell.math.OutsideVariable)1
PdeEquation (cbit.vcell.math.PdeEquation)1
ReservedVariable (cbit.vcell.math.ReservedVariable)1
SubDomain (cbit.vcell.math.SubDomain)1
Variable (cbit.vcell.math.Variable)1
