Newton Secant root. Aleks Jemcov

applications/utilities/miscellaneous/findRoot/findRoot.C

@@ -34,6 +34,7 @@ Description
 #include "IOmanip.H"
 #include "BisectionRoot.H"
 #include "RiddersRoot.H"
+#include "NewtonSecantRoot.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
@@ -50,15 +51,38 @@ public:
     }
 };
 
+
+class testFunctionDerivative
+{
+public:
+
+    testFunctionDerivative()
+    {}
+
+    scalar operator()(const scalar& x) const
+    {
+        return 0.5*Foam::pow(x,-1.5) - Foam::cos(x);
+    }
+};
+
+
 int main(int argc, char *argv[])
 {
     testFunction           tf;
+    testFunctionDerivative df;
 
     Info<< setprecision(10)
         << "Bisection root "
         << BisectionRoot<testFunction>(tf, 1e-5).root(0, 10) << nl
         << "Ridders root "
-        << RiddersRoot<testFunction>(tf, 1e-5).root(0, 10) << endl;
+        << RiddersRoot<testFunction>(tf, 1e-5).root(0, 10) << nl
+        << "NewtonSecant root "
+        << NewtonSecantRoot<testFunction,testFunctionDerivative>
+           (
+               tf,
+               df,
+               1e-5
+           ).root(1.5) << endl;
 
 
     Info<< "End\n" << endl;

src/ODE/findRoot/NewtonSecantRoot/NewtonSecantRoot.C

@@ -0,0 +1,105 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright held by original author
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software; you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by the
+    Free Software Foundation; either version 2 of the License, or (at your
+    option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM; if not, write to the Free Software Foundation,
+    Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+Class
+    NewtonSecantRoot
+
+Description
+    NewtonSecant root finder for better stability.
+    Function is provided as a template parameter function object, evaluated
+    using operator()(const scalar x)
+
+Author
+    Aleksandar Jemcov.  All rights reserved.
+
+\*---------------------------------------------------------------------------*/
+
+#include "NewtonSecantRoot.H"
+
+// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
+
+template<typename Func, typename Deriv>
+const Foam::label Foam::NewtonSecantRoot<Func,Deriv>::maxIter = 60;
+
+
+// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
+
+template<typename Func, typename Deriv>
+Foam::NewtonSecantRoot<Func,Deriv>::NewtonSecantRoot
+(
+    const Func& f,
+    const Deriv& d,
+    const scalar eps
+)
+:
+    f_(f),
+    d_(d),
+    eps_(eps)
+{}
+
+
+// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
+
+template<typename Func, typename Deriv>
+Foam::scalar Foam::NewtonSecantRoot<Func,Deriv>::root
+(
+    scalar xN
+) const
+{
+    if (0 == d_(xN))
+    {
+        FatalErrorIn
+        (
+            "Foam::scalar Foam::NewtonSecantRoot<Func,Deriv>::root\n"
+            "(\n"
+            "    const scalar xN,\n"
+            ") const"
+        )   << "Jacobian equal to zero.  f'(xN) = " << d_(xN)
+            << abort(FatalError);
+    }
+
+    scalar xNp1;
+
+    for (label nIter = 0; nIter < maxIter; ++nIter)
+    {
+        scalar fN = this->f_(xN);
+        scalar dN = this->d_(xN);
+        scalar dx = fN/dN;
+
+        scalar xBar = xN - dx;
+
+        xNp1 = xN - fN*fN/(dN*(fN - f_(xBar)));
+        if (mag(xN - xNp1) <= this->eps_)
+        {
+            return xNp1;
+        }
+
+        xN = xNp1;
+    }
+
+    return xNp1;
+}
+
+
+// ************************************************************************* //

src/ODE/findRoot/NewtonSecantRoot/NewtonSecantRoot.H

@@ -0,0 +1,108 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright held by original author
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software; you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by the
+    Free Software Foundation; either version 2 of the License, or (at your
+    option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM; if not, write to the Free Software Foundation,
+    Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+Class
+    NewtonSecantRoot
+
+Description
+    NewtonSecant root is based on combination of Newton and Secant methods.
+    Function and the funciton derivative are provided as a template parameter
+    function object, evaluated using operator()(const scalar x)
+
+Author
+    Aleksandar Jemcov.  All rights reserved.
+
+SourceFiles
+    NewtonSecantRoot.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef NewtonSecantRoot_H
+#define NewtonSecantRoot_H
+
+#include "scalar.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+                           Class NewtonSecantRoot Declaration
+\*---------------------------------------------------------------------------*/
+
+template<typename Func, typename Deriv>
+class NewtonSecantRoot
+{
+    // Private data
+
+        //- Reference to a function
+        const Func&  f_;
+
+        //- Reference to a derivative
+        const Deriv& d_;
+
+        //- Required accuracy
+        const scalar eps_;
+
+
+public:
+
+    // Static data members
+
+        //- Maximum number of iterations
+        static const label maxIter;
+
+
+    // Constructors
+
+        //- Construct given a function
+        NewtonSecantRoot(const Func& f, const Deriv& d, const scalar eps);
+
+
+    // Destructor - default
+
+
+    // Member Functions
+
+        //- Return root
+        scalar root(scalar xN) const;
+};
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#ifdef NoRepository
+#   include "NewtonSecantRoot.C"
+#endif
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //