Dual reciprocity BEM for time-stepping approach to the transient heat conduction problem in nonlinear materials

Boundary element solution of the two-dimensional sine-Gordon equation using continuous linear elements

“…For some examples of these problems, see Refs. [12][13][14][15][16][17][18] and other references therein. In this report, we adapt this approach for twodimensional sine-Gordon (SG) equation.…”

A time-stepping DRBEM for transient heat conduction in anisotropic solids

“…A similar solution for the nonlinear problems in isotropic solids was discussed in detail in Ref. [7], and the present paper is an extension of that solution procedure for those in nonlinear, anisotropic solids. The time derivative is approximated by the time-stepping scheme, and then the problem is solved by a step-by-step method and within a given time-step in an iterative manner.…”

“…The boundarydomain element method [5] is one of such solution techniques. Recently, the dual reciprocity approximation [4,6] has been attracting attention, and the present authors have so far contributed a series of papers in this respect [7,8].…”

Development and implementation of some BEM variants—A critical review

“…Apart from Poisson-type equation, DRBEM is also employed for integral equation involving biharmonic operator r 4 , especially structural analysis of plates like bending problem [118], buckling problem [65], large deflection problem [255] and vibration problem [54]. Moreover, the application of DRBEM to date has successfully been implemented in areas including heat conduction problems [12,22,234,[244][245][246][265][266][267], heat convection problem [41], convective-diffusive heat problem [228,229], fluid flow problems governed by the Navier-Stokes equation [42,70] and crack problem [7,252]. As DRBEM proved to have practical applicability, it was later extended to three dimensional problems [1,73,250].…”