57 citations · 252 across the 26 of their papers we have counts for
26 papers
Reconstruction of shear modulus inclusions in elastostatics via divergence-free localization
Henrik Garde, Nuutti Hyvönen, Valter Pohjola
We formulate an improved version of the monotonicity method for shape reconstruction in the inverse problem of linear elastostatics. We show that this method can reconstruct inclus…
Regularity and non-degeneracy of implies regularity of the fixed boundary
Henrik Garde, Michael S. Vogelius
For a diffeomorphism of a domain onto itself, which is the identity on , we prove that local regularity of the push-forward implies local regul…
Direct reconstruction of general elastic inclusions
Sarah Eberle-Blick, Henrik Garde, Nuutti Hyvönen
The inverse problem of linear elasticity is to determine the Lamé parameters, which characterize the mechanical properties of a domain, from pairs of pressure activations and the r…
Linearization-based direct reconstruction for EIT using triangular Zernike decompositions
Antti Autio, Henrik Garde, Markus Hirvensalo +1
This work implements and numerically tests the direct reconstruction algorithm introduced in [Garde & Hyvönen, SIAM J. Math. Anal., 2024] for two-dimensional linearized electrical…
Reconstruction of cracks in Calderón's inverse conductivity problem using energy comparisons
Henrik Garde, Michael Vogelius
We derive exact reconstruction methods for cracks consisting of unions of Lipschitz hypersurfaces in the context of Calderón's inverse conductivity problem. Our first method obtain…
Discrete approximations to Dirichlet and Neumann Laplacians on a half-space and norm resolvent convergence
Horia Cornean, Henrik Garde, Arne Jensen
We extend recent results on discrete approximations of the Laplacian in with norm resolvent convergence to the corresponding results for Dirichlet and Neumann Laplac…
Series reversion for electrical impedance tomography with modeling errors
Henrik Garde, Nuutti Hyvönen, Topi Kuutela
This work extends the results of [Garde and Hyvönen, Math. Comp. 91:1925-1953] on series reversion for Calderón's problem to the case of realistic electrode measurements, with both…
Linearised Calderón problem: Reconstruction and Lipschitz stability for infinite-dimensional spaces of unbounded perturbations
Henrik Garde, Nuutti Hyvönen
We investigate a linearised Calderón problem in a two-dimensional bounded simply connected domain . After extending the linearised problem for perturbations,…
Discrete approximations to Dirac operators and norm resolvent convergence
Horia D. Cornean, Henrik Garde, Arne Jensen
We consider continuous Dirac operators defined on , , together with various discrete versions of them. Both forward-backward and symmetric finite diffe…
Simplified reconstruction of layered materials in EIT
Henrik Garde
This short note considerably simplifies a reconstruction method by the author (Comm. PDE, 45(9):1118--1133, 2020), for reconstructing piecewise constant layered conductivities (PCL…
Reconstruction of singular and degenerate inclusions in Calderón's problem
Henrik Garde, Nuutti Hyvönen
We consider the reconstruction of the support of an unknown perturbation to a known conductivity coefficient in Calderón's problem. In a previous result by the authors on monotonic…
Series reversion in Calderón's problem
Henrik Garde, Nuutti Hyvönen
This work derives explicit series reversions for the solution of Calderón's problem. The governing elliptic partial differential equation is in a bounded…
Norm resolvent convergence of discretized Fourier multipliers
Horia Cornean, Henrik Garde, Arne Jensen
We prove norm estimates for the difference of resolvents of operators and their discrete counterparts, embedded into the continuum using biorthogonal Riesz sequences. The estimates…
Mimicking relative continuum measurements by electrode data in two-dimensional electrical impedance tomography
Henrik Garde, Nuutti Hyvönen
This paper introduces a constructive method for approximating relative continuum measurements in two-dimensional electrical impedance tomography based on data originating from eith…
Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography
Valentina Candiani, Jérémi Dardé, Henrik Garde +1
The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the meth…
Optimal depth-dependent distinguishability bounds for electrical impedance tomography in arbitrary dimension
Henrik Garde, Nuutti Hyvönen
The inverse problem of electrical impedance tomography is severely ill-posed. In particular, the resolution of images produced by impedance tomography deteriorates as the distance…
Reconstruction of piecewise constant layered conductivities in electrical impedance tomography
Henrik Garde
This work presents a new constructive uniqueness proof for Calderón's inverse problem of electrical impedance tomography, subject to local Cauchy data, for a large class of piecewi…
On regularity of the logarithmic forward map of electrical impedance tomography
Henrik Garde, Nuutti Hyvönen, Topi Kuutela
This work considers properties of the logarithm of the Neumann-to-Dirichlet boundary map for the conductivity equation in a Lipschitz domain. It is shown that the mapping from the…
Magnetic pseudodifferential operators represented as generalized Hofstadter-like matrices
Horia D. Cornean, Henrik Garde, Benjamin Støttrup +1
First, we reconsider the magnetic pseudodifferential calculus and show that for a large class of non-decaying symbols, their corresponding magnetic pseudodifferential operators can…
A local directional growth estimate of the resolvent norm
Horia D. Cornean, Henrik Garde, Arne Jensen +1
We study the resolvent norm of a certain class of closed linear operators on a Hilbert space, including unbounded operators with compact resolvent. It is shown that for any point i…
The regularized monotonicity method: detecting irregular indefinite inclusions
Henrik Garde, Stratos Staboulis
In inclusion detection in electrical impedance tomography, the support of perturbations (inclusion) from a known background conductivity is typically reconstructed from idealized c…
Comparison of linear and non-linear monotononicity-based shape reconstruction using exact matrix characterizations
Henrik Garde
Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction metho…
Distinguishability revisited: depth dependent bounds on reconstruction quality in electrical impedance tomography
Henrik Garde, Kim Knudsen
The reconstruction problem in electrical impedance tomography is highly ill-posed, and it is often observed numerically that reconstructions have poor resolution far away from the…
Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography
Henrik Garde, Stratos Staboulis
The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from bounda…