The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid Mechanics

We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and ID NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested by enforcing the condition of polynomial reproduction whilst deriving the shape functions. Nevertheless, given the higher complexity in forming the knotclouds for tetrahedral elements especially when higher demand is placed on the order of continuity of the shape functions across inter-element boundaries, we presently emphasize an exploration of the triangular prism based formulation in the context of several benchmark problems of interest in linear solid mechanics. In the absence of a more rigorous study on the convergence analyses, the numerical exercise, reported herein, helps establish the method as one of remarkable accuracy and robust performance against numerical ill-conditioning (such as locking of different kinds) vis-a-vis the conventional FEM.

Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units

Diffuse optical tomographic image reconstruction uses advanced numerical models that are computationally costly to be implemented in the real time. The graphics processing units (GPUs) offer desktop massive parallelization that can accelerate these computations. An open-source GPU-accelerated linear algebra library package is used to compute the most intensive matrix-matrix calculations and matrix decompositions that are used in solving the system of linear equations. These open-source functions were integrated into the existing frequency-domain diffuse optical image reconstruction algorithms to evaluate the acceleration capability of the GPUs (NVIDIA Tesla C 1060) with increasing reconstruction problem sizes. These studies indicate that single precision computations are sufficient for diffuse optical tomographic image reconstruction. The acceleration per iteration can be up to 40, using GPUs compared to traditional CPUs in case of three-dimensional reconstruction, where the reconstruction problem is more underdetermined, making the GPUs more attractive in the clinical settings. The current limitation of these GPUs in the available onboard memory (4 GB) that restricts the reconstruction of a large set of optical parameters, more than 13, 377. (C) 2010 Society of Photo-Optical Instrumentation Engineers. DOI: 10.1117/1.3506216]

A general procedure for modified crack closure integral in 3D problems with cracks

In linear elastic fracture mechanics (LEFM), Irwin's crack closure integral (CCI) is one of the signficant concepts for the estimation of strain energy release rates (SERR) G, in individual as well as mixed-mode configurations. For effective utilization of this concept in conjunction with the finite element method (FEM), Rybicki and Kanninen [Engng Fracture Mech. 9, 931 938 (1977)] have proposed simple and direct estimations of the CCI in terms of nodal forces and displacements in the elements forming the crack tip from a single finite element analysis instead of the conventional two configuration analyses. These modified CCI (MCCI) expressions are basically element dependent. A systematic derivation of these expressions using element stress and displacement distributions is required. In the present work, a general procedure is given for the derivation of MCCI expressions in 3D problems with cracks. Further, a concept of sub-area integration is proposed which facilitates evaluation of SERR at a large number of points along the crack front without refining the finite element mesh. Numerical data are presented for two standard problems, a thick centre-cracked tension specimen and a semi-elliptical surface crack in a thick slab. Estimates for the stress intensity factor based on MCCI expressions corresponding to eight-noded brick elements are obtained and compared with available results in the literature.

Accelerated gradient based diffuse optical tomographic image reconstruction

Purpose: Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). Methods: DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates. Results: Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. Conclusions: We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data. (C) 2011 American Association of Physicists in Medicine. DOI: 10.1118/1.3531572]

Novel gray coded pattern for unwrapping phase in fringe projection based 3D profiling

A method to reliably extract object profiles even with height discontinuities (that leads to 2n pi phase jumps) is proposed. This method uses Fourier transform profilometry to extract wrapped phase, and an additional image formed by illuminating the object of interest by a novel gray coded pattern for phase unwrapping. Simulation results suggest that the proposed approach not only retains the advantages of the original method, but also contributes significantly in the enhancement of its performance. Fundamental advantage of this method stems from the fact that both extraction of wrapped phase and unwrapping the same were done by gray scale images. Hence, unlike the methods that use colors, proposed method doesn't demand a color CCD camera and is ideal for profiling objects with multiple colors.

Rectilinear Path Following in 3D Space

This paper addresses the problem of determining an optimal (shortest) path in three dimensional space for a constant speed and turn-rate constrained aerial vehicle, that would enable the vehicle to converge to a rectilinear path, starting from any arbitrary initial position and orientation. Based on 3D geometry, we propose an optimal and also a suboptimal path planning approach. Unlike the existing numerical methods which are computationally intensive, this optimal geometrical method generates an optimal solution in lesser time. The suboptimal solution approach is comparatively more efficient and gives a solution that is very close to the optimal one. Due to its simplicity and low computational requirements this approach can be implemented on an aerial vehicle with constrained turn radius to reach a straight line with a prescribed orientation as required in several applications. But, if the distance between the initial point and the straight line to be followed along the vertical axis is high, then the generated path may not be flyable for an aerial vehicle with limited range of flight path angle and we resort to a numerical method for obtaining the optimal solution. The numerical method used here for simulation is based on multiple shooting and is found to be comparatively more efficient than other methods for solving such two point boundary value problem.

Some results and approaches for reconstruction conjectures

Tutte (1979) proved that the disconnected spanning subgraphs of a graph can be reconstructed from its vertex deck. This result is used to prove that if we can reconstruct a set of connected graphs from the shuffled edge deck (SED) then the vertex reconstruction conjecture is true. It is proved that a set of connected graphs can be reconstructed from the SED when all the graphs in the set are claw-free or all are P-4-free. Such a problem is also solved for a large subclass of the class of chordal graphs. This subclass contains maximal outerplanar graphs. Finally, two new conjectures, which imply the edge reconstruction conjecture, are presented. Conjecture 1 demands a construction of a stronger k-edge hypomorphism (to be defined later) from the edge hypomorphism. It is well known that the Nash-Williams' theorem applies to a variety of structures. To prove Conjecture 2, we need to incorporate more graph theoretic information in the Nash-Williams' theorem.

Electronic structure of early 3d-transition-metal oxides by analysis of the 2p core-level photoemission spectra

The electronic structures of a wide range of early transition-metal (TM) compounds, including Ti and V oxides with metal valences ranging from 2+ to 5+ and formal d-electron numbers ranging from 0 to 2, have been investigated by a configuration-interaction cluster model analysis of the core-level metal 2p x-ray photoemission spectra (XPS). Inelastic energy-loss backgrounds calculated from experimentally measured electron-energy-loss spectra (EELS) were subtracted from the XPS spectra to remove extrinsic loss features. Parameter values deduced for the charge-transfer energy Delta and the d-d Coulomb repulsion energy U are shown to continue the systematic trends established previously for the late TM compounds, giving support to a charge-transfer mechanism for the satellite structures. The early TM compounds are characterized by a large metal d-ligand p hybridization energy, resulting in strong covalency in these compounds. Values for Delta and U suggest that many early TM compounds should be reclassified as intermediate between the charge-transfer regime and the Mott-Hubbard regime.

Image reconstruction from incomplete projections data: A multiresolution modeling approach

Computerized tomography is an imaging technique which produces cross sectional map of an object from its line integrals. Image reconstruction algorithms require collection of line integrals covering the whole measurement range. However, in many practical situations part of projection data is inaccurately measured or not measured at all. In such incomplete projection data situations, conventional image reconstruction algorithms like the convolution back projection algorithm (CBP) and the Fourier reconstruction algorithm, assuming the projection data to be complete, produce degraded images. In this paper, a multiresolution multiscale modeling using the wavelet transform coefficients of projections is proposed for projection completion. The missing coefficients are then predicted based on these models at each scale followed by inverse wavelet transform to obtain the estimated projection data.

Some results on the reconstruction problems. p-claw-free, chordal, and p4-reducible graphs

A claw is an induced subgraph isomorphic to K-1,K-3. The claw-point is the point of degree 3 in a claw. A graph is called p-claw-free when no p-cycle has a claw-point on it. It is proved that for p greater than or equal to 4, p-claw-free graphs containing at least one chordless p-cycle are edge reconstructible. It is also proved that chordal graphs are edge reconstructible. These two results together imply the edge reconstructibility of claw-free graphs. A simple proof of vertex reconstructibility of P-4-reducible graphs is also presented. (C) 1995 John Wiley and Sons, Inc.

Exact complex-wave reconstruction in digital holography

We address the problem of exact complex-wave reconstruction in digital holography. We show that, by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave intensity higher than that of the object, one can achieve exact complex-wave reconstruction in the absence of noise. A feature of the proposed technique is that the zero-order artifact, which is commonly encountered in hologram reconstruction, can be completely suppressed in the absence of noise. The technique is noniterative and nonlinear. We also establish a connection between the reconstruction technique and homomorphic signal processing, which enables an interpretation of the technique from the perspective of deconvolution. Another key contribution of this paper is a direct link between the reconstruction technique and the two-dimensional Hilbert transform formalism proposed by Hahn. We show that this connection leads to explicit Hilbert transform relations between the magnitude and phase of the complex wave encoded in the hologram. We also provide results on simulated as well as experimental data to validate the accuracy of the reconstruction technique. (C) 2011 Optical Society of America

Magnetism in MnPSe3: a layered 3d(5) antiferromagnet with unusually large XY anisotropy

The anisotropic magnetic susceptibilities of single crystals of the isostructural layered antiferromagnets, MnPS3 (T-N = 78 K) and MnPSe3 (T-N = 74 K), have been measured as functions of temperature. In both compounds, divalent manganese is present in the high-spin S = 5/2 state. The anisotropies in the susceptibilities of the two are, however, very different; while the susceptibility of MnPS3 is isotropic, that of MnPSe3 shows a large XY anisotropy, unusual for a manganese compound. The anisotropic susceptibilities are described by the zero-field spin Hamiltonian: H = DSiz2 - Sigma J(ij).(S) over right arrow (S) over right arrow(j) with the quadratic single-ion anisotropy term introducing anisotropy in an otherwise isotropic situation. The exchange J and the single-ion zero-field-splitting (ZFS) parameter D were evaluated using the correlated effective-field theory of Lines. For MnPSe3, J/k = -5.29 K and D/k = 26.6 K, while for isotropic MnPS3, J/k = -8.1 K. It is suggested that the large value of the ZFS parameter for MnPSe3 as compared to MnPS3 could be due to the large ligand spin-orbit contribution of the heavier selenium.

Artifact-free reconstruction from off-axis digital holograms through nonlinear filtering

We present experimental investigation of a new reconstruction method for off-axis digital holographic microscopy (DHM). This method effectively suppresses the object auto-correlation, commonly called the zero-order term, from holographic measurements, thereby suppressing the artifacts generated by the intensities of the two beams employed for interference from complex wavefield reconstruction. The algorithm is based on non-linear filtering, and can be applied to standard DHM setups, with realistic recording conditions. We study the applicability of the technique under different experimental configurations, such as topographic images of microscopic specimens or speckle holograms.

Reconstructing Solid Model from 2D Scanned Images of Biological Organs for Finite Element Simulation

This work presents a methodology to reconstruct 3D biological organs from image sequences or other scan data using readily available free softwares with the final goal of using the organs (3D solids) for finite element analysis. The methodology deals with issues such as segmentation, conversion to polygonal surface meshes, and finally conversion of these meshes to 3D solids. The user is able to control the detail or the level of complexity of the solid constructed. The methodology is illustrated using 3D reconstruction of a porcine liver as an example. Finally, the reconstructed liver is imported into the commercial software ANSYS, and together with a cyst inside the liver, a nonlinear analysis performed. The results confirm that the methodology can be used for obtaining 3D geometry of biological organs. The results also demonstrate that the geometry obtained by following this methodology can be used for the nonlinear finite element analysis of organs. The methodology (or the procedure) would be of use in surgery planning and surgery simulation since both of these extensively use finite elements for numerical simulations and it is better if these simulations are carried out on patient specific organ geometries. Instead of following the present methodology, it would cost a lot to buy a commercial software which can reconstruct 3D biological organs from scanned image sequences.

Understanding the building-up process of three dimensional open-framework metal phosphates: Acid degradation of the 3D structures to lower dimensional structures

Acid degradation of 3D zinc phosphates primarily yields a one-dimensional ladder compound, an observation that is significant considering that the latter forms 3D structures on heating in water.