Zhang, Haiwen

[["dc.bibliographiccitation.firstpage","2271"],["dc.bibliographiccitation.issue","5"],["dc.bibliographiccitation.journal","SIAM Journal on Applied Mathematics"],["dc.bibliographiccitation.lastpage","2298"],["dc.bibliographiccitation.volume","80"],["dc.contributor.author","Zhang, Bo"],["dc.contributor.author","Zhang, Haiwen"],["dc.date.accessioned","2020-11-10T10:23:53Z"],["dc.date.available","2020-11-10T10:23:53Z"],["dc.date.issued","2020"],["dc.identifier.doi","10.1137/19M1280612"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/68629"],["dc.relation.issn","0036-1399"],["dc.relation.issn","1095-712X"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.title","An Approximate Factorization Method for Inverse Acoustic Scattering with Phaseless Total-Field Data"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.subtype","original_ja"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","489"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Inverse Problems and Imaging"],["dc.bibliographiccitation.lastpage","510"],["dc.bibliographiccitation.volume","14"],["dc.contributor.author","Xu, Xiaoxu"],["dc.contributor.author","Zhang, Bo"],["dc.contributor.author","Zhang, Haiwen"],["dc.date.accessioned","2020-07-31T08:24:05Z"],["dc.date.available","2020-07-31T08:24:05Z"],["dc.date.issued","2020"],["dc.description.abstract","This paper is concerned with uniqueness results in inverse acoustic and electromagnetic scattering problems with phaseless total-field data at a fixed frequency. We use superpositions of two point sources as the incident fields at a fixed frequency and measure the modulus of the acoustic total-field (called phaseless acoustic near-field data) on two spheres containing the scatterers generated by such incident fields on the two spheres. Based on this idea, we prove that the impenetrable bounded obstacle or the index of refraction of an inhomogeneous medium can be uniquely determined from the phaseless acoustic near-field data at a fixed frequency. Moreover, the idea is also applied to the electromagnetic case, and it is proved that the impenetrable bounded obstacle or the index of refraction of an inhomogeneous medium can be uniquely determined by the phaseless electric near-field data at a fixed frequency, that is, the modulus of the tangential component with the orientations eϕ and eθ, respectively, of the electric total-field measured on a sphere enclosing the scatters and generated by superpositions of two electric dipoles at a fixed frequency located on the measurement sphere and another bigger sphere with the polarization vectors eϕ and eθ, respectively. As far as we know, this is the first uniqueness result for three-dimensional inverse electromagnetic scattering with phaseless near-field data."],["dc.identifier.doi","10.3934/ipi.2020023"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/67502"],["dc.language.iso","en"],["dc.relation.issn","1930-8345"],["dc.title","Uniqueness in inverse acoustic and electromagnetic scattering with phaseless near-field data at a fixed frequency"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","A3673"],["dc.bibliographiccitation.issue","6"],["dc.bibliographiccitation.journal","SIAM Journal on Scientific Computing"],["dc.bibliographiccitation.lastpage","A3702"],["dc.bibliographiccitation.volume","41"],["dc.contributor.author","Qu, Fenglong"],["dc.contributor.author","Zhang, Bo"],["dc.contributor.author","Zhang, Haiwen"],["dc.date.accessioned","2020-07-31T08:13:21Z"],["dc.date.available","2020-07-31T08:13:21Z"],["dc.date.issued","2019"],["dc.description.abstract","This paper is concerned with direct and inverse scattering by a locally perturbed infinite plane (called a locally rough surface in this paper) on which a Neumann boundary condition is imposed. A novel integral equation formulation is proposed for the direct scattering problem which is defined on a bounded curve (consisting of a bounded part of the infinite plane containing the local perturbation and the lower part of a circle) with two corners and some closed smooth artificial curve. It is a nontrivial extension of our previous work on direct and inverse scattering by a locally rough surface from the Dirichlet boundary condition to the Neumann boundary condition [SIAM J. Appl. Math., 73 (2013), pp. 1811--1829]. For the Dirichlet boundary condition, the integral equation obtained is uniquely solvable in the space of bounded continuous functions on the bounded curve, and it can be solved efficiently by using the Nyström method with a graded mesh. However, the Neumann condition case leads to an integral equation which is solvable in the space of squarely integrable functions on the bounded curve rather than in the space of bounded continuous functions, making the integral equation very difficult to solve numerically with the classic and efficient Nyström method. In this paper, we make use of the recursively compressed inverse preconditioning method developed by Helsing to solve the integral equation which is efficient and capable of dealing with large wave numbers. For the inverse problem, it is proved that the locally rough surface is uniquely determined from a knowledge of the far-field pattern corresponding to incident plane waves. Moreover, based on the novel integral equation formulation, a Newton iteration method is developed to reconstruct the locally rough surface from a knowledge of multiple frequency far-field data. Numerical examples are also provided to illustrate that the reconstruction algorithm is stable and accurate even for the case of multiple-scale profiles."],["dc.identifier.doi","10.1137/19M1240745"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/67501"],["dc.language.iso","en"],["dc.relation.eissn","1095-7197"],["dc.relation.issn","1064-8275"],["dc.title","A Novel Integral Equation for Scattering by Locally Rough Surfaces and Application to the Inverse Problem: The Neumann Case"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","045009"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Inverse Problems"],["dc.bibliographiccitation.volume","29"],["dc.contributor.author","Zhang, Haiwen"],["dc.contributor.author","Zhang, Bo"],["dc.date.accessioned","2020-07-31T08:31:10Z"],["dc.date.available","2020-07-31T08:31:10Z"],["dc.date.issued","2013"],["dc.description.abstract","This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves from a penetrable and a buried obstacle. By introducing a related transmission scattering problem, a Newton iteration method is proposed to simultaneously reconstruct both the penetrable interface and the buried obstacle inside from far-field data. The main feature of our method is that we do not need to know the type of boundary conditions on the buried obstacle. In particular, the boundary condition on the buried obstacle can also be determined simultaneously by the method. Finally, numerical examples using multi-frequency data are carried out to illustrate the effectiveness of our method."],["dc.identifier.doi","10.1088/0266-5611/29/4/045009"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/67503"],["dc.language.iso","en"],["dc.relation.eissn","1361-6420"],["dc.relation.issn","0266-5611"],["dc.title","A Newton method for a simultaneous reconstruction of an interface and a buried obstacle from far-field data"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dspace.entity.type","Publication"]]