The determination of heat sources in two dimensional inverse steady heat problems by means of the method of fundamental solutions

Solutions of boundary detection problem for modified Helmholtz equation by Trefftz method

“…On the boundary C with known spatial position, over-prescribed Cauchy boundary conditions, described in Equations (2) and (3), are given. On the boundary c with unknown spatial position, only one of the Dirichlet or Neumann boundary condition is given, Equation (4) or (5). The spatial position of c is unknown in advance.…”

“…Many numerical schemes are recently proposed to deal with the inverse problems, such as the method of fundamental solutions, [1][2][3][4][5] the boundary element method (BEM), [6,7] the radial basis function collocation method, [8,9] the boundary particle method [10,11], the modified collocation Trefftz method (MCTM), [12][13][14] boundary integral equation, [15,16] etc. Most numerical schemes for inverse problems will result in illposed, inaccurate and unstable results.…”

Iterative algorithm for solving the inverse heat conduction problems with the unknown source function

“…in papers [12][13][14][15][16][17][18][19]. It is worth to mention the method of fundamental solutions supplemented by the singular value decomposition algorithm (see [13] in this connection).…”

Identification of time-dependent coefficients of heat transfer by the method of suboptimal stage-by-stage optimization

“…In particular, in the theory and practice, the conjugate gradient method of residual functional minimization [2,[5][6][7] is wide used for solving IHCP. For linear models of transfer, classical approaches [1,5] are developed that are based on the combination of the regularization technique and different notions of fundamental solutions [8]. The development of a new so-called Li-group shooting method for solving some classes of IHCP is presented in [9].…”