The Galerkin boundary element solution for thermal radiation problems

Li, B.Q.; Cui, Xiang; Song, Suping

doi:10.1016/j.enganabound.2004.01.009

Cited by 10 publications

(3 citation statements)

References 8 publications

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“…Based on the alternative formulation of [25], Sun [24] developed a modified boundary element method for the thermal radiation problems. Li et al [20] adopted the Galerkin boundary element method to discretize the thermal radiation problem without scattering. Altac [3], [4] used a singularity removal method to calculate the surface and volume integrals from the RITEs model.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical and numerical analysis of radiative heat transfer in semi-transparent media

Han¹,

Nie²,

Yuan³

2019

Appl.Math.

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Section: Introductionmentioning

confidence: 99%

“…But the discrete distribution of Gaussian nodes contributes an additional (but unnecessary) error in this step. The algorithm proposed in [20] is based on the Galerkin boundary element method. It is well-known [7] that the Galerkin method requires the computation of surface and volume double integrations.…”

Section: Introductionmentioning

confidence: 99%

Mathematical and numerical analysis of radiative heat transfer in semi-transparent media

Han¹,

Nie²,

Yuan³

2019

Appl.Math.

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“…Accordingly, an adaptive numerical integration algorithm can save computation time where possible and provide accuracy where required, by adapting the density of integration points to the local non-linearity. Being originally developed to resolve non-smooth integrands, adaptive numerical integration now finds general application in the Boundary Element Method, as (near)singular integrands are typical for the boundary element matrices [17][18][19]. Adaptive numerical integration similarly finds its way into the eXtended Finite Element Method [20].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Kronrod–Patterson integration of non‐linear finite element matrices

Janssen

2009

Numerical Meth Engineering

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Efficient simulation of unsaturated moisture flow in porous media is of great importance in many engineering fields. The highly non-linear character of unsaturated flow typically gives sharp moving moisture fronts during wetting and drying of materials with strong local moisture permeability and capacity variations as result. It is shown that such conflict with the common preference for low-order numerical integration in finite-element simulations of unsaturated moisture flow: inaccurate numerical integration leads to errors that are often far more important than errors from inappropriate discretisation. In response, this paper develops adaptive integration, based on nested Kronrod-Patterson-Gauss integration schemes: basically, the integration order is adapted to the locally observed grade of non-linearity. Adaptive integration is developed based on a standard infiltration problem, and it is demonstrated that serious reductions in the numbers of required integration points and discretisation nodes can be obtained, thus significantly increasing computational efficiency. The multidimensional applicability is exemplified with two-dimensional wetting and drying applications. While developed for finite-element unsaturated moisture transfer simulation, adaptive integration is similarly applicable for other non-linear problems and other discretisation methods. And whereas perhaps outperformed by mesh-adaptive techniques, adaptive integration requires much less implementation and computation. Both techniques can moreover be easily combined.

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External Radiative Heat Transfer

Computational Fluid and Solid Mechanics

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The Galerkin boundary element solution for thermal radiation problems

Cited by 10 publications

References 8 publications

Mathematical and numerical analysis of radiative heat transfer in semi-transparent media

Mathematical and numerical analysis of radiative heat transfer in semi-transparent media

Adaptive Kronrod–Patterson integration of non‐linear finite element matrices

External Radiative Heat Transfer

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