A study of the speed and the accuracy of the Boundary Element Method as applied to the computational simulation of biological organs

In this work, first a Fortran code is developed for three dimensional linear elastostatics using constant boundary elements; the code is based on a MATLAB code developed by the author earlier. Next, the code is parallelized using BLACS, MPI, and ScaLAPACK. Later, the parallelized code is used to demonstrate the usefulness of the Boundary Element Method (BEM) as applied to the realtime computational simulation of biological organs, while focusing on the speed and accuracy offered by BEM. A computer cluster is used in this part of the work. The commercial software package ANSYS is used to obtain the `exact' solution against which the solution from BEM is compared; analytical solutions, wherever available, are also used to establish the accuracy of BEM. A pig liver is the biological organ considered. Next, instead of the computer cluster, a Graphics Processing Unit (GPU) is used as the parallel hardware. Results indicate that BEM is an interesting choice for the simulation of biological organs. Although the use of BEM for the simulation of biological organs is not new, the results presented in the present study are not found elsewhere in the literature. Also, a serial MATLAB code, and both serial and parallel versions of a Fortran code, which can solve three dimensional (3D) linear elastostatic problems using constant boundary elements, are provided as supplementary files that can be freely downloaded.

A Study of Speed of the Boundary Element Method as applied to the Realtime Computational Simulation of Biological Organs

In this work, possibility of simulating biological organs in realtime using the Boundary Element Method (BEM) is investigated. Biological organs are assumed to follow linear elastostatic material behavior, and constant boundary element is the element type used. First, a Graphics Processing Unit (GPU) is used to speed up the BEM computations to achieve the realtime performance. Next, instead of the GPU, a computer cluster is used. Results indicate that BEM is fast enough to provide for realtime graphics if biological organs are assumed to follow linear elastostatic material behavior. Although the present work does not conduct any simulation using nonlinear material models, results from using the linear elastostatic material model imply that it would be difficult to obtain realtime performance if highly nonlinear material models that properly characterize biological organs are used. Although the use of BEM for the simulation of biological organs is not new, the results presented in the present study are not found elsewhere in the literature.

REDUCING COMPUTATIONAL EFFORT IN SOLVING GEOMECHANICS PROBLEMS WITH UPPER BOUND FINITE ELEMENTS LIMIT ANALYSIS AND LINEAR OPTIMIZATION

This paper presents a simple technique for reducing the computational effort while solving any geotechnical stability problem by using the upper bound finite element limit analysis and linear optimization. In the proposed method, the problem domain is discretized into a number of different regions in which a particular order (number of sides) of the polygon is chosen to linearize the Mohr-Coulomb yield criterion. A greater order of the polygon needs to be selected only in that region wherein the rate of the plastic strains becomes higher. The computational effort required to solve the problem with this implementation reduces considerably. By using the proposed method, the bearing capacity has been computed for smooth and rough strip footings and the results are found to be quite satisfactory.

Wave propagation analysis in laminated composite plates with transverse cracks using the wavelet spectral finite element method

This paper presents a newly developed wavelet spectral finite element (WFSE) model to analyze wave propagation in anisotropic composite laminate with a transverse surface crack penetrating part-through the thickness. The WSFE formulation of the composite laminate, which is based on the first-order shear deformation theory, produces accurate and computationally efficient results for high frequency wave motion. Transverse crack is modeled in wavenumber-frequency domain by introducing bending flexibility of the plate along crack edge. Results for tone burst and impulse excitations show excellent agreement with conventional finite element analysis in Abaqus (R). Problems with multiple cracks are modeled by assembling a number of spectral elements with cracks in frequency-wavenumber domain. Results show partial reflection of the excited wave due to crack at time instances consistent with crack locations. (C) 2014 Elsevier B.V. All rights reserved.

Mixed finite elements for electromagnetic analysis

The occurrence of spurious solutions is a well-known limitation of the standard nodal finite element method when applied to electromagnetic problems. The two commonly used remedies that are used to address this problem are (i) The addition of a penalty term with the penalty factor based on the local dielectric constant, and which reduces to a Helmholtz form on homogeneous domains (regularized formulation); (ii) A formulation based on a vector and a scalar potential. Both these strategies have some shortcomings. The penalty method does not completely get rid of the spurious modes, and both methods are incapable of predicting singular eigenvalues in non-convex domains. Some non-zero spurious eigenvalues are also predicted by these methods on non-convex domains. In this work, we develop mixed finite element formulations which predict the eigenfrequencies (including their multiplicities) accurately, even for nonconvex domains. The main feature of the proposed mixed finite element formulation is that no ad-hoc terms are added to the formulation as in the penalty formulation, and the improvement is achieved purely by an appropriate choice of finite element spaces for the different variables. We show that the formulation works even for inhomogeneous domains where `double noding' is used to enforce the appropriate continuity requirements at an interface. For two-dimensional problems, the shape of the domain can be arbitrary, while for the three-dimensional ones, with our current formulation, only regular domains (which can be nonconvex) can be modeled. Since eigenfrequencies are modeled accurately, these elements also yield accurate results for driven problems. (C) 2014 Elsevier Ltd. All rights reserved.

An interior penalty method for distributed optimal control problems governed by the biharmonic operator

In this paper, a C-0 interior penalty method has been proposed and analyzed for distributed optimal control problems governed by the biharmonic operator. The state and adjoint variables are discretized using continuous piecewise quadratic finite elements while the control variable is discretized using piecewise constant approximations. A priori and a posteriori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions. Numerical results justify the theoretical results obtained. The a posteriori error estimators are useful in adaptive finite element approximation and the numerical results indicate that the sharp error estimators work efficiently in guiding the mesh refinement. (C) 2014 Elsevier Ltd. All rights reserved.

Stochastic Structural Model of Rock and Soil Aggregates by Continuum-Based Discrete Element Method

This paper first presents a stochastic structural model to describe the random geometrical features of rock and soil aggregates. The stochastic structural model uses mixture ratio, rock size and rock shape to construct the microstructures of aggregates,and introduces two types of structural elements (block element and jointed element) and three types of material elements (rock element, soil element, and weaker jointed element)for this microstructure. Then, continuum-based discrete element method is used to study the deformation and failure mechanism of rock and soil aggregate through a series of loading tests. It is found that the stress-strain curve of rock and soil aggregates is nonlinear, and the failure is usually initialized from weaker jointed elements. Finally, some factors such as mixture ratio, rock size and rock shape are studied in detail. The numerical results are in good agreement with in situ test. Therefore, current model is effective for simulating the mechanical behaviors of rock and soil aggregates.

A Numerical Study for Turbulent Flow and Thermal Influence Over Inhomogenous Canopy of Roughness Elements

A large-eddy simulation with transitional structure function(TSF) subgrid model we previously proposed was performed to investigate the turbulent flow with thermal influence over an inhomogeneous canopy, which was represented as alternative large and small roughness elements. The aerodynamic and thermodynamic effects of the presence of a layer of large roughness elements were modelled by adding a drag term to the three-dimensional Navier-Stokes equations and a heat source/sink term to the scalar equation, respectively. The layer of small roughness elements was simply treated using the method as described in paper (Moeng 1984, J. Atmos Sci. 41, 2052-2062) for homogeneous rough surface. The horizontally averaged statistics such as mean vertical profiles of wind velocity, air temperature, et al., are in reasonable agreement with Gao et al.(1989, Boundary layer meteorol. 47, 349-377) field observation (homogeneous canopy). Not surprisingly, the calculated instantaneous velocity and temperature fields show that the roughness elements considerably changed the turbulent structure within the canopy. The adjustment of the mean vertical profiles of velocity and temperature was studied, which was found qualitatively comparable with Belcher et al. (2003, J Fluid Mech. 488, 369-398)'s theoretical results. The urban heat island(UHI) was investigated imposing heat source in the region of large roughness elements. An elevated inversion layer, a phenomenon often observed in the urban area (Sang et al., J Wind Eng. Ind. Aesodyn. 87, 243-258)'s was successfully simulated above the canopy. The cool island(CI) was also investigated imposing heat sink to simply model the evaporation of plant canopy. An inversion layer was found very stable and robust within the canopy.

Three-dimensional crack problem analysis using boundary element method with finite-part integrals

A set of hypersingular integral equations of a three-dimensional finite elastic solid with an embedded planar crack subjected to arbitrary loads is derived. Then a new numerical method for these equations is proposed by using the boundary element method combined with the finite-part integral method. According to the analytical theory of the hypersingular integral equations of planar crack problems, the square root models of the displacement discontinuities in elements near the crack front are applied, and thus the stress intensity factors can be directly calculated from these. Finally, the stress intensity factor solutions to several typical planar crack problems in a finite body are evaluated.

A new formulated method of a quasi-compatible finite-element and its application in fracture-mechanics

Based on the local properties of a singular field, the displacement pattern of an isoparametric element is improved and a new formulated method of a quasi-compatible finite element is proposed in this paper. This method can be used to solve various engineering problems containing singular distribution, especially, the singular field existing at the tip of cracks. The singular quasi-compatible element (SQCE) is constructed. The characteristics of the elements are analysed from various angles and many examples of calculations are performed. The results show that this method has many significant advantages, by which, the numerical analysis of brittle fracture problems can be solved.

A simple method to simulate shrinkage-induced cracking in cement-based composites by lattice-type modeling

A new numerical procedure is proposed to investigate cracking behaviors induced by mismatch between the matrix phase and aggregates due to matrix shrinkage in cement-based composites. This kind of failure processes is simplified in this investigation as a purely spontaneous mechanical problem, therefore, one main difficulty during simulating the phenomenon lies that no explicit external load serves as the drive to propel development of this physical process. As a result, it is different from classical mechanical problems and seems hard to be solved by using directly the classical finite element method (FEM), a typical kind of "load -> medium -> response" procedures. As a solution, the actual mismatch deformation field is decomposed into two virtual fields, both of which can be obtained by the classical FEM. Then the actual response is obtained by adding together the two virtual displacement fields based on the principle of superposition. Then, critical elements are detected successively by the event-by-event technique. The micro-structure of composites is implemented by employing the generalized beam (GB) lattice model. Numerical examples are given to show the effectiveness of the method, and detailed discussions are conducted on influences of material properties.

Application of the Schwinger multichannel method to multichannel studies of electronically inelastic electron-molecule collisions

We have applied the Schwinger Multichannel Method(SMC) to the study of electronically inelastic, low energy electron-molecule collisions. The focus of these studies has been the assessment of the importance of multichannel coupling to the dynamics of these excitation processes. It has transpired that the promising quality of results realized in early SMC work on such inelastic scattering processes has been far more difficult to obtain in these more sophisticated studies.

We have attempted to understand the sources of instability of the SMC method which are evident in these multichannel studies. Particular instances of such instability have been considered in detail, which indicate that linear dependence, failure of the separable potential approximation, and difficulties in converging matrix elements involving recorrelation or Q-space terms all conspire to complicate application of the SMC method to these studies. A method involving singular value decomposition(SVD) has been developed to, if not resolve these problems, at least mitigate their deleterious effects on the computation of electronically inelastic cross sections.

In conjunction with this SVD procedure, the SMC method has been applied to the study of the H_2 , H_2O, and N_2 molecules. Rydberg excitations of the first two molecules were found to be most sensitive to multichannel coupling near threshold. The (3σ_g → 1π_g ) and (1π_u → 1π_g) valence excitations of the N_2 molecule were found to be strongly influenced by the choice of channel coupling scheme at all collision energies considered in these studies.

Geochemistry and resonance ionization of platinum-group elements

Experimental studies were conducted with the goals of 1) determining the origin of Pt- group element (PGE) alloys and associated mineral assemblages in refractory inclusions from meteorites and 2) developing a new ultrasensitive method for the in situ chemical and isotopic analysis of PGE. A general review of the geochemistry and cosmochemistry of the PGE is given, and specific research contributions are presented within the context of this broad framework.

An important step toward understanding the cosmochemistry of the PGE is the determination of the origin of POE-rich metallic phases (most commonly εRu-Fe) that are found in Ca, AJ-rich refractory inclusions (CAI) in C3V meteorites. These metals occur along with γNi-Fe metals, Ni-Fe sulfides and Fe oxides in multiphase opaque assemblages. Laboratory experiments were used to show that the mineral assemblages and textures observed in opaque assemblages could be produced by sulfidation and oxidation of once homogeneous Ni-Fe-PGE metals. Phase equilibria, partitioning and diffusion kinetics were studied in the Ni-Fe-Ru system in order to quantify the conditions of opaque assemblage formation. Phase boundaries and tie lines in the Ni-Fe-Ru system were determined at 1273, 1073 and 873K using an experimental technique that allowed the investigation of a large portion of the Ni-Fe-Ru system with a single experiment at each temperature by establishing a concentration gradient within which local equilibrium between coexisting phases was maintained. A wide miscibility gap was found to be present at each temperature, separating a hexagonal close-packed εRu-Fe phase from a face-centered cubic γNi-Fe phase. Phase equilibria determined here for the Ni-Fe-Ru system, and phase equilibria from the literature for the Ni-Fe-S and Ni-Fe-O systems, were compared with analyses of minerals from opaque assemblages to estimate the temperature and chemical conditions of opaque assemblage formation. It was determined that opaque assemblages equilibrated at a temperature of ~770K, a sulfur fugacity 10 times higher than an equilibrium solar gas, and an oxygen fugacity 10⁶ times higher than an equilibrium solar gas.

Diffusion rates between -γNi-Fe and εRu-Fe metal play a critical role in determining the time (with respect to CAI petrogenesis) and duration of the opaque assemblage equilibration process. The diffusion coefficient for Ru in Ni (D^Ru_Ni) was determined as an analog for the Ni-Fe-Ru system by the thin-film diffusion method in the temperature range of 1073 to 1673K and is given by the expression:

D^Ru_Ni (cm² sec^-1) = 5.0(±0.7) x 10^-3 exp(-2.3(±0.1) x 10¹² erg mole^-1/RT) where R is the gas constant and T is the temperature in K. Based on the rates of dissolution and exsolution of metallic phases in the Ni-Fe-Ru system it is suggested that opaque assemblages equilibrated after the melting and crystallization of host CAI during a metamorphic event of ≥ 10³ years duration. It is inferred that opaque assemblages originated as immiscible metallic liquid droplets in the CAI silicate liquid. The bulk compositions of PGE in these precursor alloys reflects an early stage of condensation from the solar nebula and the partitioning of V between the precursor alloys and CAI silicate liquid reflects the reducing nebular conditions under which CAI were melted. The individual mineral phases now observed in opaque assemblages do not preserve an independent history prior to CAI melting and crystallization, but instead provide important information on the post-accretionary history of C3V meteorites and allow the quantification of the temperature, sulfur fugacity and oxygen fugacity of cooling planetary environments. This contrasts with previous models that called upon the formation of opaque assemblages by aggregation of phases that formed independently under highly variable conditions in the solar nebula prior to the crystallization of CAI.

Analytical studies were carried out on PGE-rich phases from meteorites and the products of synthetic experiments using traditional electron microprobe x-ray analytical techniques. The concentrations of PGE in common minerals from meteorites and terrestrial rocks are far below the ~100 ppm detection limit of the electron microprobe. This has limited the scope of analytical studies to the very few cases where PGE are unusually enriched. To study the distribution of PGE in common minerals will require an in situ analytical technique with much lower detection limits than any methods currently in use. To overcome this limitation, resonance ionization of sputtered atoms was investigated for use as an ultrasensitive in situ analytical technique for the analysis of PGE. The mass spectrometric analysis of Os and Re was investigated using a pulsed primary Ar⁺ ion beam to provide sputtered atoms for resonance ionization mass spectrometry. An ionization scheme for Os that utilizes three resonant energy levels (including an autoionizing energy level) was investigated and found to have superior sensitivity and selectivity compared to nonresonant and one and two energy level resonant ionization schemes. An elemental selectivity for Os over Re of ≥ 10³ was demonstrated. It was found that detuning the ionizing laser from the autoionizing energy level to an arbitrary region in the ionization continuum resulted in a five-fold decrease in signal intensity and a ten-fold decrease in elemental selectivity. Osmium concentrations in synthetic metals and iron meteorites were measured to demonstrate the analytical capabilities of the technique. A linear correlation between Os⁺ signal intensity and the known Os concentration was observed over a range of nearly 10⁴ in Os concentration with an accuracy of ~ ±10%, a millimum detection limit of 7 parts per billion atomic, and a useful yield of 1%. Resonance ionization of sputtered atoms samples the dominant neutral-fraction of sputtered atoms and utilizes multiphoton resonance ionization to achieve high sensitivity and to eliminate atomic and molecular interferences. Matrix effects should be small compared to secondary ion mass spectrometry because ionization occurs in the gas phase and is largely independent of the physical properties of the matrix material. Resonance ionization of sputtered atoms can be applied to in situ chemical analysis of most high ionization potential elements (including all of the PGE) in a wide range of natural and synthetic materials. The high useful yield and elemental selectivity of this method should eventually allow the in situ measurement of Os isotope ratios in some natural samples and in sample extracts enriched in PGE by fire assay fusion.

Phase equilibria and diffusion experiments have provided the basis for a reinterpretation of the origin of opaque assemblages in CAI and have yielded quantitative information on conditions in the primitive solar nebula and cooling planetary environments. Development of the method of resonance ionization of sputtered atoms for the analysis of Os has shown that this technique has wide applications in geochemistry and will for the first time allow in situ studies of the distribution of PGE at the low concentration levels at which they occur in common minerals.

Absolute oscillator strengths for iron, copper, cadmium and gold measured by the atomic beam method

Absolute f-values for 7 transitions in the first spectra of 4 elements have been measured using the atomic beam absorption technique. The equivalent widths of the absorption lines are measured with a photoelectric scanner and the atomic beam density is determined by continuously weighing a part of it with a sensitive automatic microbalance. The complete theory is presented and corrections are calculated to cope with gas absorption by the deposit on the microbalance pan and atoms which do not stick to the pan. An additional correction for the failure of the assumption of effusive flow in the formation of the atomic beam at large densities has been measured experimentally.

The following f-values were measured:

Fe: f_λ3720 = 0.0430 ± 8%

Cu: f_λ3247 = 0.427 ± 4.5%, f_λ3274 = 0.206 ± 4.7%, f_λ2492 = 0.0037 ± 9%

Cd: f_λ3261 = 0.00190 ± 7%, f_λ2288 = 1.38 ± 12%

Au: f_λ2428 = 0.283 ± 5.3%

Comparison with other accurately measured f-values, where they exist, shows agreement within experimental errors.

Influence of synthetic method on the properties of La0.5Ba0.5FeO3 SOFC cathode

Power Point presentado en The Energy and Materials Research Conference - EMR2015 celebrado en Madrid (España) entre el 25-27 de febrero de 2015