Ivan Georgiev

• PhD
• Professor (Associate) at Bulgarian Academy of Sciences

The subject of this study is to evaluate the performance of direct Gaussian solvers from Intel®’s MKL and the free PLASMA libraries for a 2D elastodynamic problem, containing cavities/inclusions. Several high performance math libraries are examined for Intel®’s Xeon CPUs (MKL and PLASMA (with ATLAS or MKL BLAS)) and Xeon Phi accelerators (MKL and M...

The problem of the alternative operational technique concerning effluent re-circulation in Horizontal Subsurface Flow Constructed Wetlands (HSF CW), and the possibility of this technique to remove efficiently pollutants under uncertainty, is investigated numerically in a stochastic way. Uncertain-but-bounded input-parameters are considered as inter...

The materials used for the synthesis of parent glass are 70% wt. metallurgical slag and 30% wt. industrial quartz sand. The initial batch is melted at and then quenched in water. The resulting glass frit is milled bellow 75 microns and pressed 1400 °C into “green” samples. In a next stage, they are heat treated at different temperatures with variou...

In Civil Engineering praxis, existing reinforced concrete (RC) structures are sometimes subjected to removal of structural elements degraded by environmental effects. These structures can be strengthened by cable elements (tension-ties) in order to avoid a progressive collapse. The probabilistic analysis of this problem is herewith numerically inve...

This book gathers the peer-reviewed proceedings of the 13th Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics, BGSIAM'18, held in Sofia, Bulgaria. The general theme of BGSIAM'18 was industrial and applied mathematics with particular focus on: mathematical physics, numerical analysis, high performance comp...

The anomalous (fractional) diffusion has a wide application in modeling many physical processes including superconductivity phenomena, protein diffusion within cells, diffusion through porous media, etc. The Fractional Laplacian is a non-local operator. Thus, after the discretization we get a dense system of linear equations. Solving it with tradit...

The aim of the study was to determine the impact of the resolution and texture of three‐dimensional (3D) models created through laser scanning on the measurement error (ME) of craniometric landmarks. Ten skulls were scanned at five different resolutions, and the generated 3D models were exported with and without texture. The 3D coordinates of 28 la...

Objectives The sagittal suture (SS) is assumed to be an initial site for the commencement of cranial suture closure as well as the most frequent spot of isolated craniosynostosis. The present study aimed to inspect the reorganization of the SS at the microlevel to assess the relation between its closure and aging and to establish whether it could b...

This book gathers the peer-reviewed proceedings of the 12th Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics, BGSIAM’17, held in Sofia, Bulgaria, in December 2017. The general theme of BGSIAM’17 was industrial and applied mathematics, with a particular focus on: high-performance computing, numerical meth...

The frontal bone develops as two halves, which further unite in a single bone by the closure of the mid-sagittal metopic suture, typically by the end of the first postnatal year. The frontal sinus begins to expand into the orbital and vertical plates of the frontal bone postnatally and reaches the level of the nasion by the fourth year of age. At t...

Foramen magnum (FM) has a well-protected position, which makes it of particular interest in forensic research. The aim of the study is to assess the sex differences in size and shape of FM, develop discriminant functions and logistic regression models based on the FM measurements, compare the accuracy results of the measurements obtained through di...

A computational approach is presented for the seismic response of existing Cultural Heritage industrial reinforced concrete (RC) structures, which have been degraded due to extreme actions (environmental, seismic etc.) and are to be seismically upgraded by using cable elements (tension-ties). Emphasis is given to shear effects, which are common for...

A numerical simulation concerning Total Phosphorus (TP) removal in Horizontal Subsurface Flow Constructed Wetlands (HSF CWs) is presented. For the phenomenon of absorption, a comparison between the results of a linear and a non-linear model is realized. The purpose is to investigate which one of these two adsorption models is the optimal one for th...

The study of dependence of elasticity modulus on the type, shape and structure of the fillers in the composites is an important task. By theoretical point of view, different models are developed to describe the relation between geometrical, mechanical and physical parameters of the fillers and matrix with the macroscopic effective properties of com...

BACKGROUND: The aim of the study is to measure the facial soft tissue thicknesses (STTs) in Bulgarians, to evaluate the relation of the STTs to the nutritional status, sex and bilateral asymmetry, and to examine the correlations between the separate STTs as well as between the STTs and body weight, height, and body mass index (BMI). In the present...

This book presents recent research on Advanced Computing in Industrial Mathematics, which is one of the most prominent interdisciplinary areas, bringing together mathematics, computer science, scientific computations, engineering, physics, chemistry, medicine, etc. Further, the book presents the major tools used in Industrial Mathematics, which are...

The technology of three-dimensional Bayesian tomographic reconstruction of homogeneous objects with high-density inclusions is developed. The approach is based on preliminary correction of projections by extracting the data corresponding to X-rays passing through a high-density region, and replacing it with synthesized data obtained by two-dimensio...

The discovery of rich, well preserved skull material in the latest Middle Pleistocene deposits of Mishin Kamik cave (N-W Bulgaria) presents an opportunity for a new analysis of the taxonomy and the phylogeny of the so called “small cave bears”. Not all the small cave bears known would have necessarily had a common origin, the size decrease could be...

Objectives: This study aimed to establish the frequency of the frontal sinus (FS) aplasia, to compare metopic and nonmetopic series and thus to assess the relationship between the preservation of metopic suture and FS development. Materials and methods: FSs were investigated in 230 dry skulls of adult males distributed into control (137) and met...

High Performance Computing (HPC) is required for many important applications in chemistry, computational fluid dynamics, etc., see, e.g., an overview in [1]. In this paper we shortly describe an application (a multiscale material design problem) that requires HPC for several reasons. The problem of interest is analysis of the fiber-reinforced concr...

Computed tomography is still being intensively studied and widely used to solve a number of industrial and medical applications. The simultaneous algebraic reconstruction technique (SART) and Heuristic Bayesian inference reconstruction (HBIR) are considered as advantageous iteration methods that are most suitable for improving the quality of the re...

The aim of the study was to assess the accuracy of linear measurements taken on surface models of dry mandibles generated from industrial CT data compared to the corresponding measurements taken directly on the mandibles. Ten mandibles were scanned through computed tomography. The CT scanning was performed on a Nikon XTH 225 system. The polygonal m...

Digital radiography is a powerful technique with a wide variety of applications. Using state of the art mathematical models and algorithms one can extract important information about the structure and the characteristics of the scanned object even from its low quality radiographic images, resulting e.g. from low-dose or short exposure time scanning...

The aim of this study was to establish the reliability of directly taken linear measurements on dry skulls and corresponding measurements taken on the 3D digital models created by laser scanning as well as to assess the agreement between both measuring methods. Four skulls were measured in two competitive methods—a direct measuring, based on the co...

A simplified numerical approach is presented for the simultaneous groundwater flow, geothermal energy (heat) transport and contaminant transport and removal in shallow unconfined aquifers. Emphasis is given to Biochemical Oxygen Demand (BOD) removal in Horizontal Subsurface Flow Constructed Wetlands (HSF CW), under non-isothermal conditions. The sy...

The diploic venous channels (DVCs) are tunnels in the diploë, between the outer and inner tables of the cranial bones. Because of its enclosed location, the diploic venous system is challenging to study. It has been claimed that the radiological examination provides a non-destructive, simple and accurate method to inspect DVCs. In this study, we te...

Metopic skulls possess specific distinctive characteristics in the configuration of the neurocranium. Due to the close developmental interrelation between neuro-and basicranium we assumed that the angulation of the cranial base could differ as well. This study aimed to compare the cranial base angle (CBA) in metopic and non-metopic series. The CBA...

This book presents recent research on Advanced Computing in Industrial Mathematics, which is one of the most prominent interdisciplinary areas and combines mathematics, computer science, scientific computations, engineering, physics, chemistry, medicine, etc. Further, the book presents the tools of Industrial Mathematics, which are based on mathema...

This paper proves a new approach for rapid prototyping of radio antennas through 3D printing and chemical metallization. For this purpose, a standard metal pyramidal horn prototype is compared with its 3D printed replica. Three different 3D polymer printers are tested. The printed samples are assessed nondestructively by an X-ray Industrial Compute...

In this paper we propose an iterative steepest-descent-type algorithm that is observed to converge towards the exact solution of the 0 discrete optimization problem, related to graph-Laplacian based image segmentation. Such an algorithm allows for significant additional improvements on the segmentation quality once the minimizer of the associated r...

Current developments on modeling of groundwater flow and contaminant transport and removal in the porous media of Horizontal Subsurface Flow Constructed Wetlands (HSF CWs) are first reviewed in a short way. The two usual environmental engineering approaches, the black-box and the process-based one, are briefly presented. Next, recent research resul...

Digital radiography is a powerful technique with a wide variety of applications in medicine and Non Destructive Testing. Using state of the art mathematical models and algorithms one can extract important information about the structure and the characteristics of the scanned object even from its low quality radiographic images, resulting e.g. from...

The co-occurrence of a bregmatic bone and metopism is an extremely rare finding. In the present study we investigate, compare, and describe this uncommon combination in two skulls of a child and an adult male. Both samples were from the osteological collection of the Institute of Experimental Morphology, Pathology and Anthropology with Museum, Bulg...

In the present study an attempt is made to choose an approach for non-destructive characterization of elastic modulus of laminated composites by laboratory measurements. Two dynamic methods, namely, ultrasonic and vibration methods are applied to compare and validate the nondestructive techniques and to demonstrate their advantages.

The seismic upgrading of Cultural Heritage structures under multiple earthquakes excitation, using materials and methods in the context of Sustainable Construction, is computationally investigated from the Civil Engineering praxis point of view. A numerical approach is presented for the seismic response of Cultural Heritage industrial buildings of...

A numerical simulation of Biochemical Oxygen Demand (BOD) removal in Horizontal Subsurface Flow Constructed Wetlands (HSF CW) is presented. Emphasis is given to select the optimal type of the reaction concerning the BOD removal. For this purpose, a computational investigation is realized by comparing the most usual reaction type, the first-order on...

Cerebral aneurysms are dilations of arterial walls that can grow and rupture. We present a novel simulation system of the blood flow through intracranial aneurysms including its interaction with the surrounding vessel. It enables physicians to estimate rupture risks by calculating the distribution of blood pressure, velocity and wall stresses, in o...

The aim of the study was to assess the accuracy and reliability of skull angles measured on 3D models created by laser scanning. Five skulls were measured through both conventional and digital measuring methods. The 3D models were created using a hand-held laser scanner Creaform VIUscan ™ . Seven angular characteristics were measured three times by...

The study aimed to establish the precision of linear measurements taken on 3D models of human mandibles created by computed tomography and to compare the measurement error with the one obtained for the corresponding measurements taken directly on the dry mandibles. Ten mandibles were scanned through computed tomography. The polygonal models in STL...

In this paper we perform a 2-class segmentation of a gray-scale 3D image under the restriction that the number of voxels within the phases are a priori fixed. Two parallel algorithms, based on the graph 2-Laplacian model [1] are proposed, implemented, and numerically tested.

Incorporation in concrete composition of steel macro- and micro – fiber reinforcement with structural function increases the degree of ductility of typically brittle cement-containing composites, which in some cases can replace completely or partially conventional steel reinforcement in the form of rods and meshes. Thus, that can reduce manufacturi...

The skeletal dysplasias are a large heterogeneous group of disorders characterized by generalized abnormalities of the skeleton. The severity of skeletal dysplasias ranged from individuals with normal stature and survival but early-onset osteoarthrosis to perinatal lethality. This study aimed to investigate bone remains with obvious skeletal abnorm...

A numerical investigation is presented for the seismic analysis of tall reinforced concrete (RC) Civil Engineering structures, which have been degradated due to extreme environmental actions and are strengthened by cable elements. The effects of multiple earthquakes on such RC building frames are computed. Damage indices are estimated in order to c...

We consider preconditioning methods for the systems of linear algebraic equations arising from Symmetric Interior Penalty discontinuous Galerkin (SIPG) discretization of linear elasticity problems in primal (displacement) formulation. The presented approach is a generalization of the subspace correction method studied in Ayuso et al. (A Subspace co...

A computational treatment is presented for the mathematically rigorous analysis of civil engineering structures, which have been environmentally damaged and subsequently strengthened by cable-elements. The problem is treated as an inequality one, where the governing conditions are equalities as well as inequalities. The cable behavior is considered...

We consider the discrete system resulting from mixed finite element approximation of a second-order elliptic boundary value problem with Crouzeix–Raviart non-conforming elements for the vector valued unknown function and piece-wise constants for the scalar valued unknown function. Since the mass matrix corresponding to the vector valued variables i...

In this paper we present a new construction of generalized hierarchical bases for symmetric positive definite matrices arising from discontinuous Galerkin discretization of second‐order partial differential equations (PDE) with highly varying coefficients. In the well‐established theory of hierarchical basis multilevel methods one basic assumption...

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lame...

A large-scale computational approach for groundwater flow and contaminant transport and removal in porous media is presented. Emphasis is given to remediation procedures in horizontal subsurface flow constructed wetlands. For the numerical procedure, the MODFLOW computer code family is used. Application is made for the simulation of horizontal subs...

We deal with the solution of the systems of linear algebraic equations arising from Symmetric Interior Penalty discontinuous Galerkin (SIPG) discretization of linear elasticity problems in primal (displacement) formulation. The main focus of the paper is on constructing a uniform preconditioner which is based on a natural splitting of the space of...

We study the behavior of the CBS constant as a quality measure for hierarchical two-level splittings of quadratic FEM stiffness matrices. The article is written in the spirit of [3] where the focus is on the robustness with respect to mesh and coefficient anisotropy. The considered splittings are: Differences and Aggregates (DA); First Reduce (FR);...

In this study we demonstrate how some different techniques which were introduced and studied in previous works by the authors can be integrated and extended in the construction of efficient algebraic multilevel iteration methods for more complex problems. We devise an optimal order algorithm for solving linear systems obtained from locking-free dis...

In this paper Rannacher–Turek non-conforming rotated bilinear finite elements are applied for the numerical solution of second order elliptic boundary value problems. The preconditioned conjugate gradient method is used for the iterative solution of the arising linear algebraic system Au=f. A locally optimized construction for an M-matrix approxima...

Generalizing the approach of a previous work of the authors, dealing with two-dimensional (2D) problems, we present multilevel preconditioners for three-dimensional (3D) elliptic problems discretized by a family of Rannacher Turek non-conforming finite elements. Preconditioners based on various multilevel extensions of two-level finite element meth...

Kinetics of crystal growth in non-isochemical systems is considered taking into account the changes in composition of the residual melt during the process. This leads to the formation of concentration gradients in the vicinity of the new phase. If a component acting as a network modifier is enriched in the crystalline phase, the melt at the interfa...

Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which often have an optimal order computational complexity with respect to the number of degrees of freedom of the system. Such methods were first presented in [6, 7], and are based on (recursive) two-level splittings of the fi...

In this paper algebraic two-level and multilevel preconditioning algorithms for second order elliptic boundary value problems are constructed, where the discretization is done using Rannacher-Turek non-conforming rotated trilinear finite elements. An important point to make is that in this case the finite element spaces corresponding to two success...

In the present paper we concentrate on algebraic two-level and multilevel preconditioners for symmetric positive definite problems arising from discretization by Rannacher-Turek non-conforming rotated bilinear finite elements on quadrilaterals. An important point to make is that in this case the finite element spaces corresponding to two successiv...

Rotated bilinear nonconforming finite elements are applied for the numerical solution of second order elliptic boundary value problems. The preconditioned conjugate gradient method is used for iterative solution of the arising linear algebraic system. A locally optimized construction of M-matrix approximation of the global stiffness matrix is the f...

New results about preconditioning of rotated trilinear nonconforming FEM elasticity systems in the case of mesh anisotropy are presented. The solver of the arising linear system is based on the constructed efficient preconditioner of the coupled stiffness matrix. Displacement decomposition of the stiffness matrix is used as a first step of the algo...

The studied large-scale linear problems arise from Crouzeix-Raviart non-conforming FEM approximation of second order elliptic boundary value problems. A two-level preconditioner for the case of coefficient anisotropy is analyzed. A special attention is given to the potential of the method for a parallel implementation. AMS Subject Classifications:...

New results on preconditioning of the rotated multilinear non-conforming finite element method (FEM) applied to elliptic systems in the case of mesh anisotropy are presented. The stiffness matrix is first approximated by a proper auxiliary M-matrix, and then modified incomplete factorization MIC(0) with perturbation is applied. The derived conditio...

In this paper we present a new framework for multilevel preconditioning of large sparse sys-tems of linear algebraic equations arising from the interior penalty discontinuous Galerkin ap-proximation of second-order elliptic boundary value problems. Though the focus is on a partic-ular family of rotated bilinear non-conforming (Rannacher-Turek) fini...