Heritage and early history of the boundary element method

By Alexander H. D. Cheng, Da Cheng. 2005

673 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0fc5ffb8731aa017def832ab4858a470b3f6539d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

An improved exponential transformation for nearly singular boundary element integrals in elasticity problems (2014, methodology): “Based on the modified distance function, the exponential transformation (Xie et al., 2011; Zhang et al., 2009b, 2010) can be developed to 3D BEM in a new form.”
Singular boundary method for solving plane strain elastostatic problems (2011, methodology): “As an alternative approach, the boundary element method (BEM) has long been touted to avoid such drawbacks (Brebbia, 1978; Cheng and Cheng, 2005; Cruse, 1988).”
The sinh transformation for evaluating nearly singular boundary element integrals over high-order geometry elements (2013, methodology): “Accurate evaluation of nearly singular integrals has long been troublesome in the boundary element method (BEM) [1–4].”
Poroelastodynamics: Linear Models, Analytical Solutions, and Numerical Methods (2009, neutral): “A solution in frequency domain of a finite 1-d column loaded at the top by total stress and pore pressure was presented by Cheng et al. [54] for comparison with a Boundary Element solution.”
3D-ICE: Fast compact transient thermal modeling for 3D ICs with inter-tier liquid cooling (2010, background): “Thus, the spatial derivate of temperature along the +�� direction at this surface can be approximated to a first order by setting the difference �� 8 − �� 2,8 to zero (Neumann boundary condition [ 19 ]).”
Infinite domain potential problems by a new formulation of singular boundary method (2013, methodology): “As an alternative approach, the boundary element method (BEM) [7,8] has long been touted to avoid such drawbacks because it applies the fundamental solution, which satisfies the governing equation and the boundary condition at infinity, to naturally reduce an infinite domain problem into a finite bo”
Singular boundary method for modified Helmholtz equations (2014, background): “Moreover, it should be mentioned that the present ISBM encounters a dramatic drop of numerical accuracy in the boundary-adjacent region, also known as the boundary layer effect in the literature of boundary element method [31,32].”