coupling an eulerian fluid calculation to a lagrangian solid calculation with the ghost fluid method we propose a numerical method for modeling multimaterial flows where the domain is decomposed into separate eulerian and lagrangian subdomains that is the equations are written in eulerian form in one subdomain and in lagrangian form in the other subdomain this is of interest for example when considering the effect of underwater explosions on the hull of a ship or the impact of a low speed projectile on a soft explosive target on the one hand high speed fluid flows are traditionally modeled by applying shock capturing schemes to the compressible euler equations to avoid problems associated with tangling of a lagrangian mesh on the other hand solid dynamics calculations are traditionally carried out using lagrangian numerical methods to avoid problems associated with numerical smearing in eulerian calculations we use the ghost fluid method to create accurate discretizations across the eulerian lagrangian interface the numerical method is presented in both one and two spatial dimensions three dimensional extensions to the interface coupling method are straightforward

convergence of an iterative method for total variation denoising in total variation denoising one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion several approaches based on this idea have recently been shown to be very effective particularly for denoising functions with discontinuities this paper analyzes the convergence of an iterative method for solving such problems the iterative method involves a lagged diffusivity approach in which a sequence of linear diffusion problems are solved global convergence in a finite dimensional setting is established and local convergence properties including rates and their dependence on various parameters are examined

level set and total variation regularization for elliptic inverse problems with discontinuous coefficients we propose a level set approach for elliptic inverse problems with piecewise constant coefficients the geometry of the discontinuity of the coefficient is represented implicitly by level set functions the inverse problem is solved using a variational augmented lagrangian formulation with total variation regularization of the coefficient the corresponding euler lagrange equation gives the evolution equation for the level set functions and the constant values of the coefficients we use a multiple level set representation which allows the coefficient to have multiple constant regions knowledge of the exact number of regions is not required only an upper bound is needed numerical experiments show that the method can recover coefficients with rather complicated geometries of discontinuities under moderate amount of noise in the observation data the method is also robust with respect to the initial guess for the geometry of the coefficient discontinuities

generation of anisotropic smoothness regularization filters for eit in the inverse conductivity problem as in any ill posed inverse problem regularization techniques are necessary in order to stabilize inversion a common way to implement regularization in electrical impedance tomography is to use tikhonov regularization the inverse problem is formulated as a minimization of two terms the mismatch of the measurements against the model and the regularization functional most commonly differential operators are used as regularization functionals leading to smooth solutions whenever the imaged region presents discontinuities in the conductivity distribution such as interorgan boundaries the smoothness prior is not consistent with the actual situation in these cases the reconstruction is enhanced by relaxing the smoothness constraints in the direction normal to the discontinuity in this paper we derive a method for generating gaussian anisotropic regularization filters the filters are generated on the basis of the prior structural information allowing a better reconstruction of conductivity profiles matching these priors when incorporating prior information into a reconstruction algorithm the risk is of biasing the inverse solutions toward the assumed distributions simulations show that with a careful selection of the regularization parameters the reconstruction algorithm is still able to detect conductivities patterns that violate the prior information a generalized singular value decomposition analysis of the effects of the anisotropic filters on regularization is presented in the last sections of the paper

mathematical and numerical modeling of two phase compressible flows with micro inertia a new model with full coupling between micro and macroscale motion is developed for compressible multiphase mixtures the equations of motion and the coupling microstructural equation an analogue of the rayleigh lamb equation are obtained by using the hamilton principle of stationary action in the particular case of bubbly fluids the resulting model contains eight partial differential equations one dimensional case and is unconditionally hyperbolic the equations are solved numerically by an adapted godunov method the model and methods are validated for two very different test problems the first one consists of a wave propagating in a liquid containing a small quantity of gas bubbles computed oscillating shock waves fit perfectly the experimental data then the one dimensional multiphase model is used as a reduction tool for the multidimensional interaction of a shock wave with a large bubble good agreement is again obtained

discrete equations for physical and numerical compressible multiphase mixtures we have recently proposed in 21 a compressible two phase unconditionally hyperbolic model able to deal with a wide range of applications interfaces between compressible materials shock waves in condensed multiphase mixtures homogeneous two phase flows bubbly and droplet flows and cavitation in liquids one of the difficulties of the model as always in this type of physical problems was the occurrence of non conservative products in 21 we have proposed a discretisation technique that was without any ambiguity only in the case of material interfaces not in the case of shock waves this model was extended to several space dimensions in 24 in this paper thanks to a deeper analysis of the model we propose a class of schemes that are able to converge to the correct solution even when shock waves interact with volume fraction discontinuities this analysis provides a more accurate estimate of closure terms but also an accurate resolution method for the conservative fluxes as well as non conservative terms even for situations involving discontinuous solutions the accuracy of the model and method is clearly demonstrated on a sequence of difficult test problems

an efficient primal dual interior point method for minimizing a sum of euclidean norms the problem of minimizing a sum of euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature this nonsmooth optimization problem arises in many different kinds of modern scientific applications we derive a primal dual interior point algorithm for the problem by applying newton s method directly to a system of nonlinear equations characterizing primal and dual feasibility and a perturbed complementarity condition the main work at each step consists of solving a system of linear equations the schur complement equations this schur complement matrix is not symmetric unlike in linear programming we incorporate a mehrotra type predictor corrector scheme and present some experimental results comparing several variations of the algorithm including as one option explicit symmetrization of the schur complement with a skew corrector term we also present results obtained from a code implemented to solve large sparse problems using a symmetrized schur complement this has been applied to problems arising in plastic collapse analysis with hundreds of thousands of variables and millions of nonzeros in the constraint matrix the algorithm typically finds accurate solutions in less than 50 iterations and determines physically meaningful solutions previously unobtainable

sparsity reconstruction in electrical impedance tomography we investigate the potential of sparsity constraints in the electrical impedance tomography eit inverse problem of inferring the distributed conductivity based on boundary potential measurements in sparsity reconstruction inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis this prior information is incorporated into a tikhonov type functional by including a sparsity promoting 1 penalty term the functional is minimized with an iterative soft shrinkage type algorithm in this paper the feasibility of the sparsity reconstruction approach is evaluated by experimental data from water tank measurements the reconstructions are computed both with sparsity constraints and with a more conventional smoothness regularization approach the results verify that the adoption of 1 type constraints can enhance the quality of eit reconstructions in most of the test cases the reconstructions with sparsity constraints are both qualitatively and quantitatively more feasible than that with the smoothness constraint

in vivo impedance imaging with total variation regularization we show that electrical impedance tomography eit image reconstruction algorithms with regularization based on the total variation tv functional are suitable for in vivo imaging of physiological data this reconstruction approach helps to preserve discontinuities in reconstructed profiles such as step changes in electrical properties at interorgan boundaries which are typically smoothed by traditional reconstruction algorithms the use of the tv functional for regularization leads to the minimization of a nondifferentiable objective function in the inverse formulation this cannot be efficiently solved with traditional optimization techniques such as the newton method we explore two implementations methods for regularization with the tv functional the lagged diffusivity method and the primal dual interior point method pd ipm first we clarify the implementation details of these algorithms for eit reconstruction next we analyze the performance of these algorithms on noisy simulated data finally we show reconstructed eit images of in vivo data for ventilation and gastric emptying studies in comparison to traditional quadratic regularization tv regulariza tion shows improved ability to reconstruct sharp contrasts

impedance imaging with first order tv regularization eit problem is a typical inverse problem with serious ill posedness in general regularization techniques are necessary for such ill posed inverse problems to overcome ill posedness the total variation tv regularization is widely used and it is also successfully applied to eit for realtime monitoring a fast and robust image reconstruction algorithm is required by exploiting recent advances in optimization we propose a first order tv algorithm for eit which simply consists of matrix vector multiplications and in which the sparse structure of the system can be easily exploited furthermore a typical smoothing parameter to overcome nondifferentibility of the tv term is not needed and a closed form solution can be applied in part using soft thresholding it shows a fast reconstruction in the beginning numerical experiments using simulated data and real experimental data support our claim

eit imaging regularization based on spectral graph wavelets the objective of electrical impedance tomographic reconstruction is to identify the distribution of tissue conductivity from electrical boundary conditions this is an ill posed inverse problem usually solved under the finite element method framework in previous studies standard sparse regularization was used for difference electrical impedance tomography to achieve a sparse solution however regarding elementwise sparsity standard sparse regularization interferes with the smoothness of conductivity distribution between neighboring elements and is sensitive to noise as an effect the reconstructed images are spiky and depict a lack of smoothness such unexpected artifacts are not realistic and may lead to misinterpretation in clinical applications to eliminate such artifacts we present a novel sparse regularization method that uses spectral graph wavelet transforms single scale or multiscale graph wavelet transforms are employed to introduce local smoothness on different scales into the reconstructed images the proposed approach relies on viewing finite element meshes as undirected graphs and applying wavelet transforms derived from spectral graph theory reconstruction results from simulations a phantom experiment and patient data suggest that our algorithm is more robust to noise and produces more reliable images

an inverse problems approach to mr ept image reconstruction magnetic resonance electrical properties tomography mr ept is an imaging modality that maps the spatial distribution of the electrical conductivity and permittivity using standard mri systems the presence of a body within the scanner alters the rf field and by mapping these alterations it is possible to recover the electrical properties the field is time harmonic and can be described by the helmholtz equation approximations to this equation have been previously used to estimate conductivity and permittivity in terms of first or second derivatives of rf field data using these same approximations an inverse approach to solving the mr ept problem is presented here that leverages a forward model for describing the magnitude and phase of the field within the imaging domain and a fitting approach for estimating the electrical properties distribution the advantages of this approach are that 1 differentiation of the measured data is not required thus reducing noise sensitivity and 2 different regularization schemes can be adopted depending on prior knowledge of the distribution of conductivity or permittivity leading to improved image quality to demonstrate the developed approach both quadratic qr and total variation tv regularization methods were implemented and evaluated through numerical simulation and experimentally acquired data the proposed inverse approach to mr ept reconstruction correctly identifies contrasts and accurately reconstructs the geometry in both simulations and experiments the tv regularized scheme reconstructs sharp spatial transitions which are difficult to reconstruct with other more traditional approaches

a five equation reduced model for compressible two phase flow problems this paper studies an eulerian diffuse interface model for the simulation of compressible multifluid and two phase flow problems we first show how to derive this model from a seven equation two pressure two velocity model of baer nunziato type using an asymptotic analysis in the limit of zero relaxation time we then study the mathematical properties of the system the structure of the waves the expression of the riemann s invariants and the existence of a mathematical entropy we also describe two different numerical approximation schemes for this system the first one relies on a linearized riemann solver while the second uses more heavily the mathematical structure of the system and relies on a linearization of the characteristic relations finally we present some numerical experiments and comparisons with the results obtained by the two pressure two velocity model as well as some test cases and comparisons with another five equation model recently proposed for interface computations between compressible fluids

a multiphase godunov method for compressible multifluid and multiphase flows we propose a new model and a solution method for two phase compressible flows the model involves six equations obtained from conservation principles applied to each phase completed by a seventh equation for the evolution of the volume fraction this equation is necessary to close the overall system the model is valid for fluid mixtures as well as for pure fluids the system of partial differential equations is hyperbolic hyperbolicity is obtained because each phase is considered to be compressible two difficulties arise for the solution one of the equations is written in non conservative form non conservative terms exist in the momentum and energy equations we propose robust and accurate discretisation of these terms the method solves the same system at each mesh point with the same algorithm it allows the simulation of interface problems between pure fluids as well as multiphase mixtures several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible the method provides reliable results is able to compute strong shock waves and deals with complex equations of state

a globally and quadratically convergent affine scaling method for linear e 1 problems recently various interior point algorithms related to the karmarkar algorithm have been developed for linear programming in this paper we first show how this interior point philosophy can be adapted to the linear l1 problem in which there are no feasibility constraints to yield a globally and linearly convergent algorithm we then show that the linear algorithm can be modified to provide aglobally and ultimatelyquadratically convergent algorithm this modified algorithm appears to be significantly more efficient in practise than a more straightforward interior point approach via a linear programming formulation we present numerical results to support this claim

a globally convergent method for l_p problems the l p norm discrete estimation problem min x in re n b a t x p p is troublesome when p is close to unity because the objective function approaches a nonsmooth form as p converges to one this paper presents an efficient algorithm for solving l p norm problems for all 1 leq p 2 when p 1 it is essentially the method presented by t f coleman and y li math programming 56 1992 pp 189 222 which is a globally and quadratically convergent algorithm under some nondegeneracy assumptions the existing iteratively reweighted least squares irls method can be obtained from the new approach by updating some dual multipliers in a special fashion the new method is globally convergent and it is superlinearly convergent when there is no zero residual at the solution at each iteration the main computational cost of the new method is the same as that of the irls method solving a reweighted least squares problem numerical experiments indicate that this method is significantly

a reconstruction algorithm for electrical impedance tomography based on sparsity regularization summary this paper develops a novel sparse reconstruction algorithm for the electrical impedance tomography problem of determining a conductivity parameter from boundary measurements the sparsity of the inhomogeneity with respect to a certain basis is a priori assumed the proposed approach is motivated by a tikhonov functional incorporating a sparsity promoting l1 penalty term and it allows us to obtain quantitative results when the assumption is valid a novel iterative algorithm of soft shrinkage type was proposed numerical results for several two dimensional problems with both single and multiple convex and nonconvex inclusions were presented to illustrate the features of the proposed algorithm and were compared with one conventional approach based on smoothness regularization copyright 2011 john wiley sons ltd

multiple frequency dbim twist algorithm for microwave breast imaging a novel distorted born iterative method dbim algorithm is proposed for microwave breast imaging based on the two step iterative shrinkage thresholding method we show that this implementation is more flexible and robust than using traditional krylov subspace methods such as the cgls as solvers of the ill posed linear problem this paper presents several strategies to increase the algorithm s robustness a hybrid multifrequency approach to achieve an optimal tradeoff between imaging accuracy and reconstruction stability a new approach to estimate the average breast tissues properties based on sampling along their range of possible values and running a few dbim iterations to find the minimum error and finally a new regularization strategy for the dbim method based on the l 1 norm and the pareto curve we present reconstruction examples which illustrate the benefits of these optimization strategies which have resulted in a dbim algorithm that outperforms our previous implementations for microwave breast imaging

solid fluid diffuse interface model in cases of extreme deformations diffuse interface methods have been recently proposed and successfully used for accurate compressible multi fluid computations abgrall 1 kapila et al 20 saurel et al 30 these methods deal with extended systems of hyperbolic equations involving a non conservative volume fraction equation and relaxation terms following the same theoretical frame we derive here an eulerian diffuse interface model for elastic solid compressible fluid interactions in situations involving extreme deformations elastic effects are included following the eulerian conservative formulation proposed in godunov 16 miller and colella 23 godunov and romenskii 17 plohr and plohr 27 and gavrilyuk et al 14 we apply first the hamilton principle of stationary action to derive the conservative part of the model the relaxation terms are then added which are compatible with the entropy inequality in the limit of vanishing volume fractions the euler equations of compressible fluids and a conservative hyperelastic model are recovered it is solved by a unique hyperbolic solver valid at each mesh point pure fluid pure solid and mixture cell capabilities of the model and methods are illustrated on various tests of impacts of solids moving in an ambient compressible fluid

iterative reconstruction methods using regularization and optimal current patterns in electrical impedance tomography an iterative reconstruction method which minimizes the effects of ill conditioning is discussed based on the modified newton raphson algorithm a regularization method which integrates prior information into the image reconstruction was developed this improves the conditioning of the information matrix in the modified newton raphson algorithm optimal current patterns were used to obtain voltages with maximal signal to noise ratio snr a complete finite element model fem was used for both the internal and the boundary electric fields reconstructed images from phantom data show that the use of regularization optimal current patterns and a complete fem model improves image accuracy the authors also investigated factors affecting the image quality of the iterative algorithm such as the initial guess image iteration and optimal current updating

electrical impedance tomography using level set representation and total variational regularization in this paper we propose a numerical scheme for the identification of piecewise constant conductivity coefficient for a problem arising from electrical impedance tomography the key feature of the scheme is the use of level set method for the representation of interface between domains with different values of coefficients numerical tests show that our method can recover sharp interfaces and can tolerate a relatively high level of noise in the observation data results concerning the effects of number of measurements noise level in the data as well as the regularization parameters on the accuracy of the scheme are also given

existence and uniqueness for electrode models for electric current computed tomography the following experiment is considered to a body of given conductivity a number of electrodes are attached through which current is sent on the same electrodes the resulting voltages are measured this experiment can be described by a number of mathematical models k s cheng et al ieee transactions on biomedical engineering 36 1989 pp 918 924 these models are discussed and their predictions compared with experiment in particular a model is exhibited that is capable of predicting the experimentally measured voltages to within 0 1 percent for this model existence and uniqueness of the associated electrical potential is proved

brownian bridges on riemannian manifolds we study properties of brownian bridges on a complete riemannian manifoldm letq be the law of brownian bridge fromx toy with lifetimet q is a probability measure on the space x y of continuous paths with 0 x and 1 y we prove thatq possesses the large deviation property with the rate function j x y omega frac 1 2 left int limits 0 1 left dot omega s right 2 ds rho x y 2 right we show that ifm and its metric are analytic then forany x y onm there exists a probability measure x y which is supported by a subset of the space of minimizing geodesics joiningx andy such that x y weakly in x y ast 0 we also give a complete characterization of the exact support of x y