Linear elements are least expensive finite elements for simultaneously recovering the source location and intensity in a general convection-diffusion process. However, the derivatives of the least-squares objective functional with Tikhonov regularizations are not well-defined when linear finite elements are used. In this work we provide a systematic formulation of the numerical inversion using ...

We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellmann-Feynman ...

Abstract. In this paper we present a hybrid approach to numerically solving two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is “hybrid” in that it merges a qualitative and a quantitative method to optimize the way of exploiting the a priori information on the background within the inversion...

After a review of the circle fitting issue, we recall a relatively unknown method derived from a classical geometric result. We propose an improvement of this technique by reweighting the data, iterating the procedure, and choosing at every step as the new inversion point the one diametrically opposite to the previous inversion point. © 2003 SPIE and IS&T. [DOI: 10.1117/1.1525792]

A key aspect of estimating transmissivity distributions from pumping tests is the spatial resolution of the estimation. Some assumption of spatial structure is needed to make an inversion possible. Both the nature of groundwater flow and assumed structure cause a smeared estimate. This research is focused on the how information content of the data smears the estimate. The inversion procedure ne...

The spectra of 25 inner-core-sensitive normal modes observed following eight recent major (Mw >7.5) earthquakes are inverted for anisotropic structure in the inner core, using a one-step inversion procedure. The mode data are combined with PKP(DF)^ PKP(AB) di¡erential traveltime data and the inner core is parametrized in terms of general axisymmetric anisotropy, allowing structure beyond restri...

We develop a new adaptive inversion procedure: Dataadaptive Resolution Inversion (DRI) method, which eliminates the need of selecting a parameterization prior to inversion. Instead, one performs a hierarchical search for the correct parameterization while solving a sequence of inverse problems with an increasing dimension of parameterization. A parsimonious approach to inverse problems usually ...

We propose an extension to Regularized Non-Linear Inversion (NLINV), which simultaneously reconstructs multiple images and sets of coil sensitivity profiles. This method, termed ENLIVE (Extended Non-Linear InVersion inspired by ESPIRiT), can be related to a convex relaxation of the NLINV problem subject to a low-rank constraint. From NLINV, it inherits its suitability for calibrationless and no...