Reference documentation for deal.II version GIT relicensing-660-g9ae06c0eb4 2024-05-17 13:10:02+00:00
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Classes | Public Member Functions | Private Member Functions | Private Attributes | List of all members
NonMatching::internal::QuadratureGeneratorImplementation::RootFinder Class Reference


struct  AdditionalData

Public Member Functions

 RootFinder (const AdditionalData &data=AdditionalData())
void find_roots (const std::vector< std::reference_wrapper< const Function< 1 > > > &functions, const BoundingBox< 1 > &interval, std::vector< double > &roots)

Private Member Functions

void find_roots (const Function< 1 > &function, const BoundingBox< 1 > &interval, const unsigned int recursion_depth, std::vector< double > &roots)

Private Attributes

const AdditionalData additional_data

Detailed Description

A class that attempts to find multiple distinct roots of a function, \(f(x)\), over an interval, \([l, r]\). This is done as follows. If there is a sign change in function value between the interval end points, we solve for the root. If there is no sign change, we attempt to bound the function value away from zero on \([a, b]\), to conclude that no roots exist. If we can't exclude that there are roots, we split the interval in two: \([l, (r + l) / 2]\), \([(r + l) / 2, r]\), and use the same algorithm recursively on each interval. This means that we can typically find 2 distinct roots, but not 3.

The bounds on the functions values are estimated using the function taylor_estimate_function_bounds, which approximates the function as a second order Taylor-polynomial around the interval midpoint. When we have a sign change on an interval, this class uses boost::math::tools::toms748_solve for finding roots .

Definition at line 664 of file quadrature_generator.h.

Constructor & Destructor Documentation

◆ RootFinder()

NonMatching::internal::QuadratureGeneratorImplementation::RootFinder::RootFinder ( const AdditionalData data = AdditionalData())


Definition at line 526 of file

Member Function Documentation

◆ find_roots() [1/2]

void NonMatching::internal::QuadratureGeneratorImplementation::RootFinder::find_roots ( const std::vector< std::reference_wrapper< const Function< 1 > > > &  functions,
const BoundingBox< 1 > &  interval,
std::vector< double > &  roots 

For each of the incoming functions, attempt to find the roots over the interval defined by interval and add these to roots. The returned roots will be sorted in ascending order: \(x_0 < x_1 <...\) and duplicate roots (with respect to the tolerance in AdditionalData) will be removed.

Definition at line 533 of file

◆ find_roots() [2/2]

void NonMatching::internal::QuadratureGeneratorImplementation::RootFinder::find_roots ( const Function< 1 > &  function,
const BoundingBox< 1 > &  interval,
const unsigned int  recursion_depth,
std::vector< double > &  roots 

Attempt to find the roots of the function over the interval defined by interval and add these to roots. recursion_depth holds the number of times this function has been called recursively.

Definition at line 556 of file

Member Data Documentation

◆ additional_data

const AdditionalData NonMatching::internal::QuadratureGeneratorImplementation::RootFinder::additional_data

Definition at line 729 of file quadrature_generator.h.

The documentation for this class was generated from the following files: