OuroborosBEM: a fast multi-GPU microscopic Monte Carlo simulation for gaseous detectors and charged particle dynamics

The design of gaseous detectors for accelerator, particle and nuclear physics requires simulations relying on multi-physics aspects. In fact, these simulations deal with the dynamics of a large number of charged particles interacting in a gaseous medium immersed in the electric field generated by a more or less complex assembly of electrodes and dielectric materials. We report here on a homemade software, called ouroborosbem, able to tackle the different features involved in such simulations. After solving the electrostatic problem for which a solver based on the boundary element method (BEM) has been implemented, particles are tracked and will microscopically interact with the gas medium. Dynamical effects have been included such as the electron-ion recombination process, the charging-up of the dielectric materials and other space charge effects that might alter the detector performances. These were made possible thanks to the nVidia CUDA language specifically optimised to run on Graphical Processor Units (GPUs) to minimize the computing times. Comparisons of the results obtained for parallel plate avalanche counters and GEM detectors to literature data on swarm parameters fully validate the performances of ouroborosbem. Moreover, we were able to precisely reproduce the measured gains of single and double GEM detectors as a function of the applied voltage.

Accelerating the charge inversion algorithm with hierarchical matrices for gas insulated systems

Surface charges accumulating on dielectrics during long-time operation of Gas Insulated High Voltage Direct Current (HVDC-GIS) equipments may affect the stable operation and could possibly trigger surface flashovers. In industrial applications, to quantify and identify the location of the surface charge accumulation from experimental measurements, the surface potential distribution is evaluated using, e.g., electrostatic probes, then the charge density is determined by solving an electrostatic problem based on an inversion procedure known as Charge Inversion Algorithm. The major practical limitation of such procedure is the inversion and the storage of the fully dense matrix arising from the representation via Integral Equations of the electrostatic phenomenon, resulting in O(N 3) computational complexity and O(N 2) memory requirement. In this paper it is shown how hierarchical matrices can be efficiently used to accelerate the charge inversion algorithm and, more importantly, reduce the overall memory requirement.

Semi-analytical method for evaluating shielding effectiveness of an enclosure with an aperture

The paper presents a semi-analytical method for calculating the shielding effectiveness (SE) of an enclosure with an aperture filled with a dielectric or magnetic material. The method is based on a combination of quasi-static analysis of coplanar strip lines (CPS) and an analytical model of an enclosure equivalent circuit. A simulation of a CPS is reduced to solving a simple electrostatic problem and can be performed by any available numerical method. The SE calculation can be performed using any of the existing models of an enclosure equivalent circuit. In the range up to 1 GHz, a validation of the proposed method was carried out using a standardized enclosure 300×120×300 mm3 as an example. To show the capabilities of the method, the paper presents the results of SE for enclosures with a PVC ventilation grill and a glass in the aperture. Using this method in conjunction with a previously published analytical model, the SE calculations for the enclosure with a conducting plate were also performed. The results show that the proposed method has an acceptable accuracy, and the average value of the absolute error does not exceed 6.4 dB

Effective properties of a porous inhomogeneously polarized by direction piezoceramic material with full metalized pore boundaries: Finite element analysis

This paper concerns the homogenization problems for porous piezocomposites with infinitely thin metalized pore surfaces. To determine the effective properties, we used the effective moduli method and the finite element approaches, realized in the ANSYS package. As a simple model of the representative volume, we applied a unit cell of porous piezoceramic material in the form of a cube with one spherical pore. We modeled metallization by introducing an additional layer of material with very large permittivity coefficients along the pore boundary. Then we simulated the nonuniform polarization field around the pore. For taking this effect into account, we previously solved the electrostatic problem for a porous dielectric material with the same geometric structure. From this problem, we obtained the polarization field in the porous piezomaterial; after that, we modified the material properties of the finite elements from dielectric to piezoelectric with element coordinate systems whose corresponding axes rotated along the polarization vectors. As a result, we obtained the porous unit cell of an inhomogeneously polarized piezoceramic matrix. From the solutions of these homogenization problems, we observed that the examined porous piezoceramics composite with metalized pore boundaries has more extensive effective transverse and shear piezomoduli, and effective dielectric constants compared to the conventional porous piezoceramics. The analysis also showed that the effect of the polarization field inhomogeneity is insignificant on the ordinary porous piezoceramics; however, it is more significant on the porous piezoceramics with metalized pore surfaces.

Four solutions of a two-cylinder electrostatic problem, and identities resulting from their equivalence

Summary Four distinct solutions exist for the potential distribution around two equal circular parallel conducting cylinders, charged to the same potential. Their equivalence is demonstrated, and the resulting analytical identities are discussed. The identities relate the Jacobi elliptic function $sn$, the Jacobi theta functions $\theta _1 ,~\theta _2 $ and infinite series over trigonometric and hyperbolic functions.

MODELING OF ELECTROSTATIC PROBLEM VIA A SUBPROBLEM FINITE ELEMENT METHOD

This work deals with the modeling of electrostatic problem by means of a subproblem finite element method. The aim of this paper is to present naturally the distributions of the electric scalar potential and the electric field in regions existing the various voltages or difference of voltages. The method permits to simultaneously use both node and edge elements in function spaces of the studied problem. Indeed, the distributed fields (e.g. electric scalar potential and electric field) are presented in the same function space and a week formulation written for both nodal and edge finite elements.

A Practical Approach to Large Scale Electronic Structure Calculations in Electrolyte Solutions via Continuum-Embedded Linear-Scaling DFT

We present the implementation of a hybrid continuum-atomistic model for including the effects of surrounding electrolyte in large-scale density functional theory (DFT) calculations within the ONETEP linear-scaling DFT code, which allows the simulation of large complex systems such as electrochemical interfaces. The model represents the electrolyte ions as a scalar field and the solvent as a polarisable dielectric continuum, both surrounding the quantum solute. The overall energy expression is a grand canonical functional incorporating the electron kinetic and exchange correlation energies, the total electrostatic energy, entropy and chemical potentials of surrounding electrolyte, osmotic pressure, and the effects of cavitation, dispersion and repulsion. The DFT calculation is performed fully self-consistently in the electrolyte model, allowing the quantum mechanical system and the surrounding continuum environment to interact and mutually polarize. A bespoke parallel Poisson-Boltzmann solver library, DL_MG, deals with the electrostatic problem, solving a generalized Poisson-Boltzmann equation. Our model supports open boundary conditions, which allows the treatment of molecules, entire biomolecules or larger nanoparticle assemblies in electrolyte. We have also implemented the model for periodic boundary conditions, allowing the treatment of extended systems such as electrode surfaces in contact with electrolyte. A key feature of the model is the use of solute-size and solvation-shell-aware accessibility functions that prevent the unphysical accumulation of electrolyte charge near the quantum solute boundary. The model has a small number of parameters: here we demonstrate their calibration against experimental mean activity coefficients. We also present an exemplar simulation of a 1634-atom model of the interface between a graphite anode and LiPF₆ electrolyte in ethylene carbonate solvent. We compare the cases where Li atoms are intercalated at opposite edges of the graphite slab and in solution, demonstrating a potential application of the model in simulations of fundamental processes in Li-ion batteries.

A Practical Approach to Large Scale Electronic Structure Calculations in Electrolyte Solutions via Continuum-Embedded Linear-Scaling DFT

We present the implementation of a hybrid continuum-atomistic model for including the effects of surrounding electrolyte in large-scale density functional theory (DFT) calculations within the ONETEP linear-scaling DFT code, which allows the simulation of large complex systems such as electrochemical interfaces. The model represents the electrolyte ions as a scalar field and the solvent as a polarisable dielectric continuum, both surrounding the quantum solute. The overall energy expression is a grand canonical functional incorporating the electron kinetic and exchange correlation energies, the total electrostatic energy, entropy and chemical potentials of surrounding electrolyte, osmotic pressure, and the effects of cavitation, dispersion and repulsion. The DFT calculation is performed fully self-consistently in the electrolyte model, allowing the quantum mechanical system and the surrounding continuum environment to interact and mutually polarize. A bespoke parallel Poisson-Boltzmann solver library, DL_MG, deals with the electrostatic problem, solving a generalized Poisson-Boltzmann equation. Our model supports open boundary conditions, which allows the treatment of molecules, entire biomolecules or larger nanoparticle assemblies in electrolyte. We have also implemented the model for periodic boundary conditions, allowing the treatment of extended systems such as electrode surfaces in contact with electrolyte. A key feature of the model is the use of solute-size and solvation-shell-aware accessibility functions that prevent the unphysical accumulation of electrolyte charge near the quantum solute boundary. The model has a small number of parameters: here we demonstrate their calibration against experimental mean activity coefficients. We also present an exemplar simulation of a 1634-atom model of the interface between a graphite anode and LiPF₆ electrolyte in ethylene carbonate solvent. We compare the cases where Li atoms are intercalated at opposite edges of the graphite slab and in solution, demonstrating a potential application of the model in simulations of fundamental processes in Li-ion batteries.

USING THE PATTERN EQUATIONS METHOD FOR ANALYSIS THE DIFFRACTION BY SMALL OBJECTS

Scattering of electromagnetic waves by small particles is an important key task of diffraction theory. This is due to a wide range of practical applications of the effects associated with the scattering of electromagnetic waves by particles, small in com-parison with the wavelength. From the moment of the appearance of the first papers devoted to this subject and up to the present, the most used mathematical model used in solving the problem of scattering by small bodies is the dipole approximation (Rayleigh approximation). This approach is described in sufficient detail for particular cases of scattering by balls and ellipsoids, when the solution of the auxiliary electrostatic problem can be obtained in explicit form. Note that the solution of the problem in the electrostatic approximation in the general case, in itself, is quite complicated and time-consuming compared with the solution of the original wave problem. Existing methods for solving it have a number of fundamental limitations. In this paper, we developed a technique based on the use of the method of Pattern Equations Method (PEM), first proposed in 1992. In a significant number of publications, it has been clearly demonstrated that PEM have important advantages over many alternative methods and are very effective in solving a wide class of problems. In constructing a new approach to the analysis of scattering by small bodies, we used the high convergence rate of the PEM established in our previous papers. Indeed, as shown in previous works of the authors of this article, to solve the problem of scattering by impedance bodies, whose characteristic size is comparable with the wavelength of the incident field, it suffices to take into account, depending on the polarization of the incident field, one to three terms in the Fourier decomposition of the scattering pattern. This circumstance made it possible to obtain explicit formulas for the integral scattering characteristics applicable to complex-shaped impedance scatterers. In this work, explicit formulas are obtained for the integrated scattering characteristics that are applicable to small, compared with the incident radiation wavelength, scatterers. A review is given of the application of an approximate methodology for calculating the integral scattering characteristics of small diffusers of arbitrary shape, in particular, thin dielectric cylinders, based on the use of PEM. As the above results show, the approximate relations obtained have sufficient accuracy in a wide range of problem parameters.

The self-consistent quantum-electrostatic problem in strongly non-linear regime

The self-consistent quantum-electrostatic (also known as Poisson-Schrödinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low temperatures, these fluctuations make the problem highly non-linear which renders iterative schemes deeply unstable. We present a stable algorithm that provides a solution to this problem with controlled accuracy. The technique is intrinsically convergent even in highly non-linear regimes. We illustrate our approach with both a calculation of the compressible and incompressible stripes in the integer quantum Hall regime as well as a calculation of the differential conductance of a quantum point contact geometry. Our technique provides a viable route for the predictive modeling of the transport properties of quantum nanoelectronics devices.