Public API

Integrals

MeshIntegrals.integral — Function

integral(f, geometry)
integral(f, geometry, algorithm)
integral(f, geometry, algorithm, FP)

Numerically integrate a given function f(::Point) over the domain defined by a geometry using a particular integration algorithm with floating point precision of type FP.

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Aliases

MeshIntegrals.lineintegral — Function

lineintegral(f, geometry)
lineintegral(f, geometry, algorithm)
lineintegral(f, geometry, algorithm, FP)

Numerically integrate a given function f(::Point) along a line-like geometry using a particular integration algorithm with floating point precision of type FP.

Algorithm types available:

GaussKronrod (default)
GaussLegendre
HAdaptiveCubature

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MeshIntegrals.surfaceintegral — Function

surfaceintegral(f, geometry)
surfaceintegral(f, geometry, algorithm)
surfaceintegral(f, geometry, algorithm, FP)

Numerically integrate a given function f(::Point) along a surface geometry using a particular integration algorithm with floating point precision of type FP.

Algorithm types available:

GaussKronrod
GaussLegendre
HAdaptiveCubature (default)

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MeshIntegrals.volumeintegral — Function

volumeintegral(f, geometry)
volumeintegral(f, geometry, algorithm)
volumeintegral(f, geometry, algorithm, FP)

Numerically integrate a given function f(::Point) throughout a volumetric geometry using a particular integration algorithm with floating point precision of type FP.

Algorithm types available:

GaussKronrod
GaussLegendre
HAdaptiveCubature (default)

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Integration Algorithms

MeshIntegrals.GaussKronrod — Type

GaussKronrod(kwargs...)

Numerically integrate using the h-adaptive Gauss-Kronrod quadrature rule implemented by QuadGK.jl. All standard QuadGK.quadgk keyword arguments are supported.

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MeshIntegrals.GaussLegendre — Type

GaussLegendre(n)

Numerically integrate using an n'th-order Gauss-Legendre quadrature rule. nodes and weights are efficiently calculated using FastGaussQuadrature.jl.

So long as the integrand function can be well-approximated by a polynomial of order 2n-1, this method should yield results with 16-digit accuracy in O(n) time. If the function is know to have some periodic content, then n should (at a minimum) be greater than the expected number of periods over the geometry, e.g. length(geometry)/lambda.

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MeshIntegrals.HAdaptiveCubature — Type

GaussKronrod(kwargs...)

Numerically integrate areas and surfaces using the h-adaptive cubature rule implemented by HCubature.jl. All standard HCubature.hcubature keyword arguments are supported.

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