Author(s)

J.T. Chen & H.-K. Hong

Abstract

On the relations of hypersingular kernel and divergent series in heat conduction problem using BEM J.T. Chen, H.-K. Hong Department of Civil Engineering, Taiwan University, Taipei, Taiwan ABSTRACT In this paper, the dual series representation for heat conduction problem with time-dependent boundary conditions is derived using eigenfunction expansion. Based on this formulation, the conventional kernel functions are reduced to the degenerate kernels in series form, therefore, the Hadamard(or Mangier) principal value for hypersingular kernel is transformed to the summability of divergent series in Cesaro sense or to convergent series by Stokes' transfor- mation technique. Both of the two regularization techniques are employed to make the divergent series summable to finite part with physical meaning of heat flux. Finally, an illustrative example is shown to see the validity of the dual series representation. INTRODUCTION It is well known that the elliptical field problem

Keywords