Evaluation of External Memory Access Performance on a High-End FPGA Hybrid Computer*Computation* **2016**, *4*(4), 41; doi:10.3390/computation4040041 - 25 October 2016**Abstract **

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The motivation of this research was to evaluate the main memory performance of a hybrid super computer such as the Convey HC-x, and ascertain how the controller performs in several access scenarios, vis-à-vis hand-coded memory prefetches. Such memory patterns are very useful
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The motivation of this research was to evaluate the main memory performance of a hybrid super computer such as the Convey HC-x, and ascertain how the controller performs in several access scenarios, vis-à-vis hand-coded memory prefetches. Such memory patterns are very useful in stencil computations. The theoretical bandwidth of the memory of the Convey is compared with the results of our measurements. The accurate study of the memory subsystem is particularly useful for users when they are developing their application-specific personality. Experiments were performed to measure the bandwidth between the coprocessor and the memory subsystem. The experiments aimed mainly at measuring the reading access speed of the memory from Application Engines (FPGAs). Different ways of accessing data were used in order to find the most efficient way to access memory. This way was proposed for future work in the Convey HC-x. When performing a series of accesses to memory, non-uniform latencies occur. The Memory Controller of the Convey HC-x in the coprocessor attempts to cover this latency. We measure memory efficiency as a ratio of the number of memory accesses and the number of execution cycles. The result of this measurement converges to one in most cases. In addition, we performed experiments with hand-coded memory accesses. The analysis of the experimental results shows how the memory subsystem and Memory Controllers work. From this work we conclude that the memory controllers do an excellent job, largely because (transparently to the user) they seem to cache large amounts of data, and hence hand-coding is not needed in most situations.
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A Multi-Compartment Hybrid Computational Model Predicts Key Roles for Dendritic Cells in Tuberculosis Infection*Computation* **2016**, *4*(4), 39; doi:10.3390/computation4040039 - 21 October 2016**Abstract **

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Tuberculosis (TB) is a world-wide health problem with approximately 2 billion people infected with *Mycobacterium tuberculosis* (Mtb, the causative bacterium of TB). The pathologic hallmark of Mtb infection in humans and Non-Human Primates (NHPs) is the formation of spherical structures, primarily in
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Tuberculosis (TB) is a world-wide health problem with approximately 2 billion people infected with *Mycobacterium tuberculosis* (Mtb, the causative bacterium of TB). The pathologic hallmark of Mtb infection in humans and Non-Human Primates (NHPs) is the formation of spherical structures, primarily in lungs, called granulomas. Infection occurs after inhalation of bacteria into lungs, where resident antigen-presenting cells (APCs), take up bacteria and initiate the immune response to Mtb infection. APCs traffic from the site of infection (lung) to lung-draining lymph nodes (LNs) where they prime T cells to recognize *Mtb*. These T cells, circulating back through blood, migrate back to lungs to perform their immune effector functions. We have previously developed a hybrid agent-based model (ABM, labeled *GranSim*) describing in silico immune cell, bacterial (Mtb) and molecular behaviors during tuberculosis infection and recently linked that model to operate across three physiological compartments: lung (infection site where granulomas form), lung draining lymph node (LN, site of generation of adaptive immunity) and blood (a measurable compartment). Granuloma formation and function is captured by a spatio-temporal model (i.e., ABM), while LN and blood compartments represent temporal dynamics of the whole body in response to infection and are captured with ordinary differential equations (ODEs). In order to have a more mechanistic representation of APC trafficking from the lung to the lymph node, and to better capture antigen presentation in a draining LN, this current study incorporates the role of dendritic cells (DCs) in a computational fashion into *GranSim*. **Results**: The model was calibrated using experimental data from the lungs and blood of NHPs. The addition of DCs allowed us to investigate in greater detail mechanisms of recruitment, trafficking and antigen presentation and their role in tuberculosis infection. **Conclusion**: The main conclusion of this study is that early events after Mtb infection are critical to establishing a timely and effective response. Manipulating CD8+ and CD4+ T cell proliferation rates, as well as DC migration early on during infection can determine the difference between bacterial clearance vs. uncontrolled bacterial growth and dissemination.
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Obituary for Walter Kohn (1923–2016)*Computation* **2016**, *4*(4), 40; doi:10.3390/computation4040040 - 20 October 2016**Abstract **
Walter Kohn (Figure 1) is one of the most cited scientists of our time, who died on 19 April 2016 in Santa Barbara, CA, USA. [...]
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Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers*Computation* **2016**, *4*(4), 38; doi:10.3390/computation4040038 - 17 October 2016**Abstract **

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We present an Anderson acceleration-based approach to spatially couple three-dimensional Lattice Boltzmann and Navier–Stokes (LBNS) flow simulations. This allows to locally exploit the computational features of both fluid flow solver approaches to the fullest extent and yields enhanced control to match the
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We present an Anderson acceleration-based approach to spatially couple three-dimensional Lattice Boltzmann and Navier–Stokes (LBNS) flow simulations. This allows to locally exploit the computational features of both fluid flow solver approaches to the fullest extent and yields enhanced control to match the LB and NS degrees of freedom within the LBNS overlap layer. Designed for parallel Schwarz coupling, the Anderson acceleration allows for the simultaneous execution of both Lattice Boltzmann and Navier–Stokes solver. We detail our coupling methodology, validate it, and study convergence and accuracy of the Anderson accelerated coupling, considering three steady-state scenarios: plane channel flow, flow around a sphere and channel flow across a porous structure. We find that the Anderson accelerated coupling yields a speed-up (in terms of iteration steps) of up to 40% in the considered scenarios, compared to strictly sequential Schwarz coupling.
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Computational Streetscapes*Computation* **2016**, *4*(3), 37; doi:10.3390/computation4030037 - 20 September 2016**Abstract **

Streetscapes have presented a long-standing interest in many fields. Recently, there has been a resurgence of attention on streetscape issues, catalyzed in large part by computing. Because of computing, there is more understanding, vistas, data, and analysis of and on streetscape phenomena
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Streetscapes have presented a long-standing interest in many fields. Recently, there has been a resurgence of attention on streetscape issues, catalyzed in large part by computing. Because of computing, there is more understanding, vistas, data, and analysis of and on streetscape phenomena than ever before. This diversity of lenses trained on streetscapes permits us to address long-standing questions, such as how people use information while mobile, how interactions with people and things occur on streets, how we might safeguard crowds, how we can design services to assist pedestrians, and how we could better support special populations as they traverse cities. Amid each of these avenues of inquiry, computing is facilitating new ways of posing these questions, particularly by expanding the scope of what-if exploration that is possible. With assistance from computing, consideration of streetscapes now reaches across scales, from the neurological interactions that form among place cells in the brain up to informatics that afford real-time views of activity over whole urban spaces. For some streetscape phenomena, computing allows us to build realistic but synthetic facsimiles in computation, which can function as artificial laboratories for testing ideas. In this paper, I review the domain science for studying streetscapes from vantages in physics, urban studies, animation and the visual arts, psychology, biology, and behavioral geography. I also review the computational developments shaping streetscape science, with particular emphasis on modeling and simulation as informed by data acquisition and generation, data models, path-planning heuristics, artificial intelligence for navigation and way-finding, timing, synthetic vision, steering routines, kinematics, and geometrical treatment of collision detection and avoidance. I also discuss the implications that the advances in computing streetscapes might have on emerging developments in cyber-physical systems and new developments in urban computing and mobile computing.
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An Extremely Efficient Boundary Element Method for Wave Interaction with Long Cylindrical Structures Based on Free-Surface Green’s Function*Computation* **2016**, *4*(3), 36; doi:10.3390/computation4030036 - 16 September 2016**Abstract **

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The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters in the coastal region, etc. A higher-order scheme is used to discretize geometry of
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The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters in the coastal region, etc. A higher-order scheme is used to discretize geometry of the structure as well as the physical wave potentials. As the kernel of this method, Wehausen’s free-surface Green function is calculated by a newly-developed Gauss–Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve its computation efficiency, an analytical solution is derived for a fast evaluation of the Green function that needs to be implemented thousands of times. In addition, the OpenMP parallelization technique is applied to the formation of the influence coefficient matrix, significantly reducing the running CPU time. Computations are performed on wave-exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates a good performance of the present method.
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Image Segmentation for Cardiovascular Biomedical Applications at Different Scales*Computation* **2016**, *4*(3), 35; doi:10.3390/computation4030035 - 15 September 2016**Abstract **

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In this study, we present several image segmentation techniques for various image scales and modalities. We consider cellular-, organ-, and whole organism-levels of biological structures in cardiovascular applications. Several automatic segmentation techniques are presented and discussed in this work. The overall pipeline
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In this study, we present several image segmentation techniques for various image scales and modalities. We consider cellular-, organ-, and whole organism-levels of biological structures in cardiovascular applications. Several automatic segmentation techniques are presented and discussed in this work. The overall pipeline for reconstruction of biological structures consists of the following steps: image pre-processing, feature detection, initial mask generation, mask processing, and segmentation post-processing. Several examples of image segmentation are presented, including patient-specific abdominal tissues segmentation, vascular network identification and myocyte lipid droplet micro-structure reconstruction.
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Towards TDDFT for Strongly Correlated Materials*Computation* **2016**, *4*(3), 34; doi:10.3390/computation4030034 - 10 September 2016**Abstract **

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We present some details of our recently-proposed Time-Dependent Density-Functional Theory (TDDFT) for strongly-correlated materials in which the exchange-correlation (XC) kernel is derived from the charge susceptibility obtained using Dynamical Mean-Field Theory (the TDDFT + DMFT approach). We proceed with deriving the expression
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We present some details of our recently-proposed Time-Dependent Density-Functional Theory (TDDFT) for strongly-correlated materials in which the exchange-correlation (XC) kernel is derived from the charge susceptibility obtained using Dynamical Mean-Field Theory (the TDDFT + DMFT approach). We proceed with deriving the expression for the XC kernel for the one-band Hubbard model by solving DMFT equations via two approaches, the Hirsch–Fye Quantum Monte Carlo (HF-QMC) and an approximate low-cost perturbation theory approach, and demonstrate that the latter gives results that are comparable to the exact HF-QMC solution. Furthermore, through a variety of applications, we propose a simple analytical formula for the XC kernel. Additionally, we use the exact and approximate kernels to examine the nonhomogeneous ultrafast response of two systems: a one-band Hubbard model and a Mott insulator YTiO_{3}. We show that the frequency dependence of the kernel, i.e., memory effects, is important for dynamics at the femtosecond timescale. We also conclude that strong correlations lead to the presence of beats in the time-dependent electric conductivity in YTiO_{3}, a feature that could be tested experimentally and that could help validate the few approximations used in our formulation. We conclude by proposing an algorithm for the generalization of the theory to non-linear response.
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The Influence of One-Electron Self-Interaction on *d*-Electrons*Computation* **2016**, *4*(3), 33; doi:10.3390/computation4030033 - 6 September 2016**Abstract **

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We investigate four diatomic molecules containing transition metals using two variants of hybrid functionals. We compare global hybrid functionals that only partially counteract self-interaction to local hybrid functionals that are designed to be formally free from one-electron self-interaction. As *d*-orbitals are
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We investigate four diatomic molecules containing transition metals using two variants of hybrid functionals. We compare global hybrid functionals that only partially counteract self-interaction to local hybrid functionals that are designed to be formally free from one-electron self-interaction. As *d*-orbitals are prone to be particularly strongly influenced by self-interaction errors, one may have expected that self-interaction-free local hybrid functionals lead to a qualitatively different Kohn–Sham density of states than global hybrid functionals. Yet, we find that both types of hybrids lead to a very similar density of states. For both global and local hybrids alike, the intrinsic amount of exact exchange plays the dominant role in counteracting electronic self-interaction, whereas being formally free from one-electron self-interaction seems to be of lesser importance.
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Calculation of the Acoustic Spectrum of a Cylindrical Vortex in Viscous Heat-Conducting Gas Based on the Navier–Stokes Equations*Computation* **2016**, *4*(3), 32; doi:10.3390/computation4030032 - 20 August 2016**Abstract **

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An extremely interesting problem in aero-hydrodynamics is the sound radiation of a single vortical structure. Currently, this type of problem is mainly considered for an incompressible medium. In this paper a method was developed to take into account the viscosity and thermal
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An extremely interesting problem in aero-hydrodynamics is the sound radiation of a single vortical structure. Currently, this type of problem is mainly considered for an incompressible medium. In this paper a method was developed to take into account the viscosity and thermal conductivity of gas. The acoustic radiation frequency of a cylindrical vortex on a flat wall in viscous heat-conducting gas (air) has been investigated. The problem is solved on the basis of the Navier–Stokes equations using the small initial vorticity approach. The power expansion of unknown functions in a series with a small parameter (vorticity) is used. It is shown that there are high-frequency oscillations modulated by a low-frequency signal. The value of the high frequency remains constant for a long period of time. Thus the high frequency can be considered a natural frequency of the vortex radiation. The value of the natural frequency depends only on the initial radius of the cylindrical vortex, and does not depend on the intensity of the initial vorticity. As expected from physical considerations, the natural frequency decreases exponentially as the initial radius of the cylinder increases. Furthermore, the natural frequency differs from that of the oscillations inside the initial cylinder and in the outer domain. The results of the paper may be of interest for aeroacoustics and tornado modeling.
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Computational Analysis of Natural Ventilation Flows in Geodesic Dome Building in Hot Climates*Computation* **2016**, *4*(3), 31; doi:10.3390/computation4030031 - 17 August 2016**Abstract **

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For centuries, dome roofs were used in traditional houses in hot regions such as the Middle East and Mediterranean basin due to its thermal advantages, structural benefits and availability of construction materials. This article presents the computational modelling of the wind- and
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For centuries, dome roofs were used in traditional houses in hot regions such as the Middle East and Mediterranean basin due to its thermal advantages, structural benefits and availability of construction materials. This article presents the computational modelling of the wind- and buoyancy-induced ventilation in a geodesic dome building in a hot climate. The airflow and temperature distributions and ventilation flow rates were predicted using Computational Fluid Dynamics (CFD). The three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations were solved using the CFD tool ANSYS FLUENT15. The standard k-epsilon was used as turbulence model. The modelling was verified using grid sensitivity and flux balance analysis. In order to validate the modelling method used in the current study, additional simulation of a similar domed-roof building was conducted for comparison. For wind-induced ventilation, the dome building was modelled with upper roof vents. For buoyancy-induced ventilation, the geometry was modelled with roof vents and also with two windows open in the lower level. The results showed that using the upper roof openings as a natural ventilation strategy during winter periods is advantageous and could reduce the indoor temperature and also introduce fresh air. The results also revealed that natural ventilation using roof vents cannot satisfy thermal requirements during hot summer periods and complementary cooling solutions should be considered. The analysis showed that buoyancy-induced ventilation model can still generate air movement inside the building during periods with no or very low wind.
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Electron Correlations in Local Effective Potential Theory*Computation* **2016**, *4*(3), 30; doi:10.3390/computation4030030 - 16 August 2016**Abstract **

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Local effective potential theory, both stationary-state and time-dependent, constitutes the mapping from a system of electrons in an external field to one of the noninteracting fermions possessing the same basic variable such as the density, thereby enabling the determination of the energy
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Local effective potential theory, both stationary-state and time-dependent, constitutes the mapping from a system of electrons in an external field to one of the noninteracting fermions possessing the same basic variable such as the density, thereby enabling the determination of the energy and other properties of the electronic system. This paper is a description via Quantal Density Functional Theory (QDFT) of the electron correlations that must be accounted for in such a mapping. It is proved through QDFT that independent of the form of external field, (a) it is possible to map to a model system possessing all the basic variables; and that (b) with the requirement that the model fermions are subject to the same external fields, the only correlations that must be considered are those due to the Pauli exclusion principle, Coulomb repulsion, and Correlation–Kinetic effects. The cases of both a static and time-dependent electromagnetic field, for which the basic variables are the density and physical current density, are considered. The examples of solely an external electrostatic or time-dependent electric field constitute special cases. An efficacious unification in terms of electron correlations, independent of the type of external field, is thereby achieved. The mapping is explicated for the example of a quantum dot in a magnetostatic field, and for a quantum dot in a magnetostatic and time-dependent electric field.
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DiamondTorre Algorithm for High-Performance Wave Modeling*Computation* **2016**, *4*(3), 29; doi:10.3390/computation4030029 - 12 August 2016**Abstract **

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Effective algorithms of physical media numerical modeling problems’ solution are discussed. The computation rate of such problems is limited by memory bandwidth if implemented with traditional algorithms. The numerical solution of the wave equation is considered. A finite difference scheme with a
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Effective algorithms of physical media numerical modeling problems’ solution are discussed. The computation rate of such problems is limited by memory bandwidth if implemented with traditional algorithms. The numerical solution of the wave equation is considered. A finite difference scheme with a cross stencil and a high order of approximation is used. The DiamondTorre algorithm is constructed, with regard to the specifics of the GPGPU’s (general purpose graphical processing unit) memory hierarchy and parallelism. The advantages of these algorithms are a high level of data localization, as well as the property of asynchrony, which allows one to effectively utilize all levels of GPGPU parallelism. The computational intensity of the algorithm is greater than the one for the best traditional algorithms with stepwise synchronization. As a consequence, it becomes possible to overcome the above-mentioned limitation. The algorithm is implemented with CUDA. For the scheme with the second order of approximation, the calculation performance of 50 billion cells per second is achieved. This exceeds the result of the best traditional algorithm by a factor of five.
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Highly Excited States from a Time Independent Density Functional Method*Computation* **2016**, *4*(3), 28; doi:10.3390/computation4030028 - 5 August 2016**Abstract **

A constrained optimized effective potential (COEP) methodology proposed earlier by us for singly low-lying excited states is extended to highly excited states having the same spatial and spin symmetry. Basic tenets of time independent density functional theory and its COEP implementation for
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A constrained optimized effective potential (COEP) methodology proposed earlier by us for singly low-lying excited states is extended to highly excited states having the same spatial and spin symmetry. Basic tenets of time independent density functional theory and its COEP implementation for excited states are briefly reviewed. The amended Kohn–Sham-like equations for excited state orbitals and their specific features for highly excited states are discussed. The accuracy of the method is demonstrated using exchange-only calculations for highly excited states of the He and Li atoms.
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Automatic Generation of Massively Parallel Codes from ExaSlang*Computation* **2016**, *4*(3), 27; doi:10.3390/computation4030027 - 4 August 2016**Abstract **

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Domain-specific languages (DSLs) have the potential to provide an intuitive interface for specifying problems and solutions for domain experts. Based on this, code generation frameworks can produce compilable source code. However, apart from optimizing execution performance, parallelization is key for pushing the
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Domain-specific languages (DSLs) have the potential to provide an intuitive interface for specifying problems and solutions for domain experts. Based on this, code generation frameworks can produce compilable source code. However, apart from optimizing execution performance, parallelization is key for pushing the limits in problem size and an essential ingredient for exascale performance. We discuss necessary concepts for the introduction of such capabilities in code generators. In particular, those for partitioning the problem to be solved and accessing the partitioned data are elaborated. Furthermore, possible approaches to expose parallelism to users through a given DSL are discussed. Moreover, we present the implementation of these concepts in the ExaStencils framework. In its scope, a code generation framework for highly optimized and massively parallel geometric multigrid solvers is developed. It uses specifications from its multi-layered external DSL ExaSlang as input. Based on a general version for generating parallel code, we develop and implement widely applicable extensions and optimizations. Finally, a performance study of generated applications is conducted on the JuQueen supercomputer.
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Interaction of Hydrogen with Au Modified by Pd and Rh in View of Electrochemical Applications*Computation* **2016**, *4*(3), 26; doi:10.3390/computation4030026 - 20 July 2016**Abstract **

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Hydrogen interaction with bimetallic Au(Pd) and Au(Rh) systems are studied with the density functional theory (DFT)-based periodic approach. Several bimetallic configurations with varying concentrations of Pd and Rh atoms in the under layer of a gold surface(111) were considered. The reactivity of
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Hydrogen interaction with bimetallic Au(Pd) and Au(Rh) systems are studied with the density functional theory (DFT)-based periodic approach. Several bimetallic configurations with varying concentrations of Pd and Rh atoms in the under layer of a gold surface(111) were considered. The reactivity of the doped Au(111) toward hydrogen adsorption and absorption was related to the property modifications induced by the presence of metal dopants. DFT-computed quantities, such as the energy stability, the inter-atomic and inter-slab binding energies between gold and dopants, and the charge density were used to infer the similarities and differences between both Pd and Rh dopants in these model alloys. The hydrogen penetration into the surface is favored in the bimetallic slab configurations. The underlayer dopants affect the reactivity of the surface gold toward hydrogen adsorption in the systems with a dopant underlayer, covered by absorbed hydrogen up to a monolayer. This indicates a possibility to tune the gold surface properties of bimetallic electrodes by modulating the degree of hydrogen coverage of the inner dopant layer(s).
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Predictions of Physicochemical Properties of Ionic Liquids with DFT*Computation* **2016**, *4*(3), 25; doi:10.3390/computation4030025 - 19 July 2016**Abstract **

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Nowadays, density functional theory (DFT)-based high-throughput computational approach is becoming more efficient and, thus, attractive for finding advanced materials for electrochemical applications. In this work, we illustrate how theoretical models, computational methods, and informatics techniques can be put together to form a
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Nowadays, density functional theory (DFT)-based high-throughput computational approach is becoming more efficient and, thus, attractive for finding advanced materials for electrochemical applications. In this work, we illustrate how theoretical models, computational methods, and informatics techniques can be put together to form a simple DFT-based throughput computational workflow for predicting physicochemical properties of room-temperature ionic liquids. The developed workflow has been used for screening a set of 48 ionic pairs and for analyzing the gathered data. The predicted relative electrochemical stabilities, ionic charges and dynamic properties of the investigated ionic liquids are discussed in the light of their potential practical applications.
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Orbital Energy-Based Reaction Analysis of S_{N}2 Reactions*Computation* **2016**, *4*(3), 23; doi:10.3390/computation4030023 - 8 July 2016**Abstract **

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An orbital energy-based reaction analysis theory is presented as an extension of the orbital-based conceptual density functional theory. In the orbital energy-based theory, the orbitals contributing to reactions are interpreted to be valence orbitals giving the largest orbital energy variation from reactants
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An orbital energy-based reaction analysis theory is presented as an extension of the orbital-based conceptual density functional theory. In the orbital energy-based theory, the orbitals contributing to reactions are interpreted to be valence orbitals giving the largest orbital energy variation from reactants to products. Reactions are taken to be electron transfer-driven when they provide small variations for the gaps between the contributing occupied and unoccupied orbital energies on the intrinsic reaction coordinates in the initial processes. The orbital energy-based theory is then applied to the calculations of several ${\mathrm{S}}_{\mathrm{N}}$ 2 reactions. Using a reaction path search method, the Cl^{−} + CH_{3}I → ClCH_{3} + I^{−} reaction, for which another reaction path called “roundabout path” is proposed, is found to have a precursor process similar to the roundabout path just before this S_{N}2 reaction process. The orbital energy-based theory indicates that this precursor process is obviously driven by structural change, while the successor S_{N}2 reaction proceeds through electron transfer between the contributing orbitals. Comparing the calculated results of the S_{N}2 reactions in gas phase and in aqueous solution shows that the contributing orbitals significantly depend on solvent effects and these orbitals can be correctly determined by this theory.
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On the v-Representabilty Problem in Density Functional Theory: Application to Non-Interacting Systems*Computation* **2016**, *4*(3), 24; doi:10.3390/computation4030024 - 5 July 2016**Abstract **

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Based on a computational procedure for determining the functional derivative with respect to the density of any antisymmetric *N*-particle wave function for a non-interacting system that leads to the density, we devise a test as to whether or not a wave
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Based on a computational procedure for determining the functional derivative with respect to the density of any antisymmetric *N*-particle wave function for a non-interacting system that leads to the density, we devise a test as to whether or not a wave function known to lead to a given density corresponds to a solution of a Schrödinger equation for some potential. We examine explicitly the case of non-interacting systems described by Slater determinants. Numerical examples for the cases of a one-dimensional square-well potential with infinite walls and the harmonic oscillator potential illustrate the formalism.
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Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media*Computation* **2016**, *4*(2), 22; doi:10.3390/computation4020022 - 7 June 2016**Abstract **

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We propose an online adaptive local-global POD-DEIM model reduction method for flows in heterogeneous porous media. The main idea of the proposed method is to use local online indicators to decide on the global update, which is performed via reduced cost local
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We propose an online adaptive local-global POD-DEIM model reduction method for flows in heterogeneous porous media. The main idea of the proposed method is to use local online indicators to decide on the global update, which is performed via reduced cost local multiscale basis functions. This unique local-global online combination allows (1) developing local indicators that are used for both local and global updates (2) computing global online modes via local multiscale basis functions. The multiscale basis functions consist of offline and some online local basis functions. The approach used for constructing a global reduced system is based on Proper Orthogonal Decomposition (POD) Galerkin projection. The nonlinearities are approximated by the Discrete Empirical Interpolation Method (DEIM). The online adaption is performed by incorporating new data, which become available at the online stage. Once the criterion for updates is satisfied, we adapt the reduced system online by changing the POD subspace and the DEIM approximation of the nonlinear functions. The main contribution of the paper is that the criterion for adaption and the construction of the global online modes are based on local error indicators and local multiscale basis function which can be cheaply computed. Since the adaption is performed infrequently, the new methodology does not add significant computational overhead associated with when and how to adapt the reduced basis. Our approach is particularly useful for situations where it is desired to solve the reduced system for inputs or controls that result in a solution outside the span of the snapshots generated in the offline stage. Our method also offers an alternative of constructing a robust reduced system even if a potential initial poor choice of snapshots is used. Applications to single-phase and two-phase flow problems demonstrate the efficiency of our method.
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