Solving Inverse Cauchy Problems of the Helmholtz Equation Using Conjugate Gradient Based-Method: BICG, BICGSTAB And PCG

Abstract

An inverse Cauchy problem on an under-specified portion of the boundary of a twodimensional domain occupied by a material satisfying Helmholtz-type equations from additional Cauchy data on the remaining accessible portion of the boundary has been considered. The solution is approached using a polynomial expansion to obtain a linear system; this linear system has been solved by conjugate gradient based-method. The efficiency of the proposed method has been confirmed by applying it for different examples and by comparing the obtained results by using three different numerical methods.

Keywords

• Inverse Cauchy problems, Helmholtz equation, polynomial expansion, conjugate gradient based-method.