2020
DOI: 10.1016/j.cam.2019.112463
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On a boundary integral solution of a lateral planar Cauchy problem in elastodynamics

Abstract: A boundary integral based method for the stable reconstruction of missing boundary data is presented for the governing hyperbolic equation of elastodynamics in annular planar domains. Cauchy data in the form of the solution and traction is reconstructed on the inner boundary curve from the similar data given on the outer boundary. The ill-posed data reconstruction problem is reformulated as a sequence of boundary integral equations using the Laguerre transform with respect to time and employing a single-layer … Show more

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Cited by 4 publications
(4 citation statements)
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“…, N in (4). Calculate the matrix of the recursive systems (8), where elements E 0 (x ℓj , y k ), ℓ = 1, 2, k = 1, . .…”
Section: Main Steps Of the Proposed Methodsmentioning
confidence: 99%
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“…, N in (4). Calculate the matrix of the recursive systems (8), where elements E 0 (x ℓj , y k ), ℓ = 1, 2, k = 1, . .…”
Section: Main Steps Of the Proposed Methodsmentioning
confidence: 99%
“…. , N : Generate the right-hand side vector of the system (8), where the matrices E p (x ℓj , y k ) are calculated by (6). For p > 0 the coecients ⃗ α mk , m = 0, 1, .…”
Section: Main Steps Of the Proposed Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…In section 4, we present numerical examples to clarify our approach. It is worth noting that this two-step methodology has been successfully extended to address a diverse spectrum of initial boundary value problems for parabolic and hyperbolic equations [3,5,7,8].…”
Section: Introductionmentioning
confidence: 99%