Sentence examples for using the fundamental solution from inspiring English sources
The sound field is simulated by using the boundary element method (BEM), which is a numerical technique to reduce the boundary integral equations using the fundamental solution and Green's transfer functions, for sound field analysis in this paper.
The new algorithm is based on Green's function approach by using the fundamental solution of heat conduction in semi-infinite soils and Duhamel's integral for incorporation of general boundary conditions.
After using the fundamental solution in the corresponding Green's function, one can reduce it to the BEM.
Using the fundamental solution of the heat equation, we solve the general solution of this equation and prove the Hyers-Ulam stability in the spaces of tempered distributions and Fourier hyperfunctions.
Also, using the fundamental solution of the heat equation, we obtain the general solution and prove the Hyers-Ulam stability of this equation in the spaces of generalized functions such as tempered distributions and Fourier hyperfunctions.
Using the fundamental solution of the heat equation, we solve the general solution and prove the Hyers-Ulam stability of this equation in the spaces of tempered distributions and Fourier hyperfunctions.
More numerical comparisons also show that using the particular solutions is more advantageous than using the fundamental solutions in both HTM and CTM.
Besides, the adopted method also avoids using the fundamental solutions of anisotropic materials and overcomes the difficulties of solving the inclusions with irregular shapes in the BEM.
Using the fundamental solutions and recurrence formulas developed in this paper, the mode shape function of vibration of a non-uniform beam with an arbitrary number of cracks and concentrated masses can be easily determined.
Using the fundamental solutions of each step rod and a recurrence formula developed in this paper, a new exact approach for determining the longitudinal natural frequencies and mode shapes of multi-step non-uniform rods is proposed.
Using the fundamental solutions for three-dimensional transversely isotropic magnetoelectroelastic bimaterials, the extended displacements at any point for an internal crack parallel to the interface in a magnetoelectroelastic bimaterial are expressed in terms of the extended displacement discontinuities across the crack surfaces.
