Proceedings of the 7th International Conference on Numerical Methods and Applications, 2010
We deal with the solution of the systems of linear algebraic equations arising from Symmetric Int... more 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 piecewise linear discontinuous functions. The presented approach has recently been introduced in [2] in the context of designing subspace correction methods for scalar elliptic partial differential equations and is extended here to linear elasticity equations, i.e., a class of vector field problems. Similar to the scalar case the solution of the linear algebraic system corresponding to the SIPG method is reduced to the solution of a problem arising from discretization by nonconforming Crouzeix-Raviart elements plus the solution of a well-conditioned problem on the complementary space.
In this study we demonstrate how some different techniques which were introduced and studied in p... more 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 discretization of 3D pure displacement elasticity problems. The presented
ABSTRACT In this paper we present a new construction of generalized hierarchical bases for symmet... more ABSTRACT 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 is that the PDE coefficients are smooth functions on the elements of the coarsest mesh partition. It is shown numerically that the developed hierarchical bases yields a robust splitting with respect to jump discontinuities of the PDE coefficient at arbitrary element interfaces on the finest mesh.
Computer Assisted Mechanics and Engineering Sciences
New results about preconditioning of rotated trilinear nonconforming FEM elasticity systems in th... more 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 algorithm. At the second step, modified incomplete factorization MIC(0) with perturbation is applied to a proper auxiliary M-matrix to get an approximate factorization of the obtained block-diagonal matrix. The derived condition number estimates and the presented numerical tests well illustrate the behaviour of the theoretically studied algorithms as well as their robustness for some more realistic benchmark problems.
The cytokine macrophage migration inhibitory factor (MIF) plays a critical role in inflammatory d... more The cytokine macrophage migration inhibitory factor (MIF) plays a critical role in inflammatory diseases and atherogenesis. We identify the chemokine receptors CXCR2 and CXCR4 as functional receptors for MIF. MIF triggered G ai -and integrin-dependent arrest and chemotaxis of monocytes and T cells, rapid integrin activation and calcium influx through CXCR2 or CXCR4. MIF competed with cognate ligands for CXCR4 and CXCR2 binding, and directly bound to CXCR2. CXCR2 and CD74 formed a receptor complex, and monocyte arrest elicited by MIF in inflamed or atherosclerotic arteries involved both CXCR2 and CD74. In vivo, Mif deficiency impaired monocyte adhesion to the arterial wall in atherosclerosis-prone mice, and MIF-induced leukocyte recruitment required Il8rb (which encodes Cxcr2). Blockade of Mif but not of canonical ligands of Cxcr2 or Cxcr4 in mice with advanced atherosclerosis led to plaque regression and reduced monocyte and T-cell content in plaques. By activating both CXCR2 and CXCR4, MIF displays chemokine-like functions and acts as a major regulator of inflammatory cell recruitment and atherogenesis. Targeting MIF in individuals with manifest atherosclerosis can potentially be used to treat this condition.
In this paper we present a new framework for multilevel preconditioning of large sparse systems o... more In this paper we present a new framework for multilevel preconditioning of large sparse systems of linear algebraic equations arising from the interior penalty discontinuous Galerkin approximation of second-order elliptic boundary value problems. Though the focus is on a particular family of rotated bilinear non-conforming (Rannacher-Turek) finite elements in two space dimensions (2D) the proposed rather general setting is neither limited to this particular choice of elements nor to 2D problems Under the assumption that the finest partition is a result of multilevel refinement of a given coarse mesh, we develop a novel concept for the hierarchical splitting of the unknowns. Next we show how the constant in the strengthened Cauchy-Bunyakowski-Schwarz (CBS) inequality can be estimated locally in this setting. Two basic problems are studied: the scalar elliptic equation and the Lamé system of linear elasticity. This part of the presented theoretical results is in the spirit of algebraic multilevel iteration (AMLI) methods.
The purpose of this paper was to review the organisational structures among farm producers within... more The purpose of this paper was to review the organisational structures among farm producers within the EC Market and East European Countries (EEC). The main emphasis was on organisational structures rather than the entrepreneurs. More explicit attention was focused on the buyer and seller relationship in the upstream segment of the food processing industry. We found numerous impediments in the bargaining processes from the purchasing firms' negotiations for resources in foodstuffs. This paper hypothesises that the causes for this imbalance in transactual trades are due to: (1) ownership structural differences; (2) buyer and seller bargaining power inequalities. Such industry characteristics warrant careful examination.
Downloadable! The purpose of this paper is to show the way for increasing the local capacity for ... more Downloadable! The purpose of this paper is to show the way for increasing the local capacity for public discussion in the sphere of environmental protection in the municipalities of South East part of Bulgaria. Target groups are representatives of local authorities, municipal administrations ...
The purpose of this study was to investigate the effect of dietary fish oil and krill oil supplem... more The purpose of this study was to investigate the effect of dietary fish oil and krill oil supplementation on paraoxonase activity (PON1) in a rabbit model of obesity.
The numerical homogenization of anisotropic linear elastic materials with strongly heterogeneous ... more The numerical homogenization of anisotropic linear elastic materials with strongly heterogeneous microstructure is studied. The developed algorithm is applied to the case of two-phase composite material: epoxy resin based nanocomposite incorporating nanoclay Cloisite. The upscaling procedure is described in terms of six auxiliary elastic problems for the reference volume element (RVE). A parallel PCG method is implemented for efficient solution of the arising large-scale systems with sparse, symmetric, and positive semidefinite matrices. Then, the bulk modulus tensor is computed from the upscaled stiffness tensor and its eigenvectors are used to define the transformation matrix. The stiffness tensor of the material is transformed with respect to the principle directions of anisotropy (PDA) which gives a canonical (unique) representation of the material properties. Numerical upscaling results are shown. The voxel microstructure of the two-phase composite material is extracted from a high resolution computed tomography image.
The dynamics of cluster growth in a two-lane driven diffusive system is analyzed by extensive Mon... more The dynamics of cluster growth in a two-lane driven diffusive system is analyzed by extensive Monte Carlo simulations. We observe good dynamical scaling for small values of a particle-particle exchange probability γ on relatively small lattices. As γ increases, the (effective) scaling exponents develop a dependence on γ, suggesting that the observed coarsening does not result in a genuine ordered
We deal with the solution of the systems of linear algebraic equations arising from Symmetric Int... more 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 piecewise linear discontinuous functions. The presented approach has recently been introduced in [2] in the context of designing subspace correction methods for scalar elliptic partial differential equations and is extended here to linear elasticity equations, i.e., a class of vector field problems. Similar to the scalar case the solution of the linear algebraic system corresponding to the SIPG method is reduced to the solution of a problem arising from discretization by nonconforming Crouzeix-Raviart elements plus the solution of a well-conditioned problem on the complementary space.
Grigorova, N., Zh. Ivanova, E. Dichlianova, T. Georgieva, T. Slavov, E. Vachkova & I. Penchev Geo... more Grigorova, N., Zh. Ivanova, E. Dichlianova, T. Georgieva, T. Slavov, E. Vachkova & I. Penchev Georgiev, 2015. The effect of antioxidant treatment on blood lactate and pyruvate concentrations in a rabbit model of obesity. Bulg. J. Vet. Med. (online first). In the current study, the impact of dietary antioxidant supplementation on fasting blood lactate and pyruvate concentrations in a rabbit model of obesity was investigated. A total of 26 rabbits were randomly divided into 3 groups: castrated and obese animals (CO, n=7); castrated, obese and treated with antioxidants (Immunoprotect, n=7, CIm) and non-castrated, non-treated controls (NC, n=12). At the end of the 2-month treatment period blood lactate concentration, lactate to pyruvate and lactate to glucose ratio in CIm were significantly (P<0.05) lower than in NC and tended to be lower than in CO. No group differences in pyruvate and glucose concentrations were found. There was a significant negative (r =–0.53; P<0.05) correlat...
ABSTRACT The structure of the honeycomb-like three-dimensional networks formed on self-assembly o... more ABSTRACT The structure of the honeycomb-like three-dimensional networks formed on self-assembly of the tetradentate ligand 1,2-bis(5′-dipyrimidyl)ethyne with copper (I) iodide and copper (I) bromide are presented.
We present precision Monte Carlo data and analytic arguments for an asymmetric exclusion process,... more We present precision Monte Carlo data and analytic arguments for an asymmetric exclusion process, involving two species of particles driven in opposite directions on a 2 × L lattice. We propose a scenario which resolves a stark discrepancy between earlier simulation data, suggesting the existence of an ordered phase, and an analytic conjecture according to which the system should revert to a disordered state in the thermodynamic limit. By analyzing the finite size effects in detail, we argue that the presence of a single, seemingly macroscopic, cluster is an intermediate stage of a complex nucleation process: In smaller systems, this cluster is destabilized while larger systems allow the formation of multiple clusters. Both limits lead to exponential cluster size distributions which are, however, controlled by very different length scales.
Journal of Physics A: Mathematical and General, 2006
Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening pheno... more Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening phenomena in a simple driven diffusive system. The model is reminiscent of vehicular traffic on a two-lane ring road. At sufficiently high density, the system develops jams (clusters) which coarsen with time. A key parameter is the passing probability, γ. For small values of γ, the growing clusters display dynamic scaling, with a growth exponent of 2/3. For larger values of γ, the growth exponent must be adjusted, suggesting the ordered (jammed) state is not a genuine phase but rather a finite size effect.
Proceedings of the 7th International Conference on Numerical Methods and Applications, 2010
We deal with the solution of the systems of linear algebraic equations arising from Symmetric Int... more 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 piecewise linear discontinuous functions. The presented approach has recently been introduced in [2] in the context of designing subspace correction methods for scalar elliptic partial differential equations and is extended here to linear elasticity equations, i.e., a class of vector field problems. Similar to the scalar case the solution of the linear algebraic system corresponding to the SIPG method is reduced to the solution of a problem arising from discretization by nonconforming Crouzeix-Raviart elements plus the solution of a well-conditioned problem on the complementary space.
In this study we demonstrate how some different techniques which were introduced and studied in p... more 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 discretization of 3D pure displacement elasticity problems. The presented
ABSTRACT In this paper we present a new construction of generalized hierarchical bases for symmet... more ABSTRACT 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 is that the PDE coefficients are smooth functions on the elements of the coarsest mesh partition. It is shown numerically that the developed hierarchical bases yields a robust splitting with respect to jump discontinuities of the PDE coefficient at arbitrary element interfaces on the finest mesh.
Computer Assisted Mechanics and Engineering Sciences
New results about preconditioning of rotated trilinear nonconforming FEM elasticity systems in th... more 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 algorithm. At the second step, modified incomplete factorization MIC(0) with perturbation is applied to a proper auxiliary M-matrix to get an approximate factorization of the obtained block-diagonal matrix. The derived condition number estimates and the presented numerical tests well illustrate the behaviour of the theoretically studied algorithms as well as their robustness for some more realistic benchmark problems.
The cytokine macrophage migration inhibitory factor (MIF) plays a critical role in inflammatory d... more The cytokine macrophage migration inhibitory factor (MIF) plays a critical role in inflammatory diseases and atherogenesis. We identify the chemokine receptors CXCR2 and CXCR4 as functional receptors for MIF. MIF triggered G ai -and integrin-dependent arrest and chemotaxis of monocytes and T cells, rapid integrin activation and calcium influx through CXCR2 or CXCR4. MIF competed with cognate ligands for CXCR4 and CXCR2 binding, and directly bound to CXCR2. CXCR2 and CD74 formed a receptor complex, and monocyte arrest elicited by MIF in inflamed or atherosclerotic arteries involved both CXCR2 and CD74. In vivo, Mif deficiency impaired monocyte adhesion to the arterial wall in atherosclerosis-prone mice, and MIF-induced leukocyte recruitment required Il8rb (which encodes Cxcr2). Blockade of Mif but not of canonical ligands of Cxcr2 or Cxcr4 in mice with advanced atherosclerosis led to plaque regression and reduced monocyte and T-cell content in plaques. By activating both CXCR2 and CXCR4, MIF displays chemokine-like functions and acts as a major regulator of inflammatory cell recruitment and atherogenesis. Targeting MIF in individuals with manifest atherosclerosis can potentially be used to treat this condition.
In this paper we present a new framework for multilevel preconditioning of large sparse systems o... more In this paper we present a new framework for multilevel preconditioning of large sparse systems of linear algebraic equations arising from the interior penalty discontinuous Galerkin approximation of second-order elliptic boundary value problems. Though the focus is on a particular family of rotated bilinear non-conforming (Rannacher-Turek) finite elements in two space dimensions (2D) the proposed rather general setting is neither limited to this particular choice of elements nor to 2D problems Under the assumption that the finest partition is a result of multilevel refinement of a given coarse mesh, we develop a novel concept for the hierarchical splitting of the unknowns. Next we show how the constant in the strengthened Cauchy-Bunyakowski-Schwarz (CBS) inequality can be estimated locally in this setting. Two basic problems are studied: the scalar elliptic equation and the Lamé system of linear elasticity. This part of the presented theoretical results is in the spirit of algebraic multilevel iteration (AMLI) methods.
The purpose of this paper was to review the organisational structures among farm producers within... more The purpose of this paper was to review the organisational structures among farm producers within the EC Market and East European Countries (EEC). The main emphasis was on organisational structures rather than the entrepreneurs. More explicit attention was focused on the buyer and seller relationship in the upstream segment of the food processing industry. We found numerous impediments in the bargaining processes from the purchasing firms' negotiations for resources in foodstuffs. This paper hypothesises that the causes for this imbalance in transactual trades are due to: (1) ownership structural differences; (2) buyer and seller bargaining power inequalities. Such industry characteristics warrant careful examination.
Downloadable! The purpose of this paper is to show the way for increasing the local capacity for ... more Downloadable! The purpose of this paper is to show the way for increasing the local capacity for public discussion in the sphere of environmental protection in the municipalities of South East part of Bulgaria. Target groups are representatives of local authorities, municipal administrations ...
The purpose of this study was to investigate the effect of dietary fish oil and krill oil supplem... more The purpose of this study was to investigate the effect of dietary fish oil and krill oil supplementation on paraoxonase activity (PON1) in a rabbit model of obesity.
The numerical homogenization of anisotropic linear elastic materials with strongly heterogeneous ... more The numerical homogenization of anisotropic linear elastic materials with strongly heterogeneous microstructure is studied. The developed algorithm is applied to the case of two-phase composite material: epoxy resin based nanocomposite incorporating nanoclay Cloisite. The upscaling procedure is described in terms of six auxiliary elastic problems for the reference volume element (RVE). A parallel PCG method is implemented for efficient solution of the arising large-scale systems with sparse, symmetric, and positive semidefinite matrices. Then, the bulk modulus tensor is computed from the upscaled stiffness tensor and its eigenvectors are used to define the transformation matrix. The stiffness tensor of the material is transformed with respect to the principle directions of anisotropy (PDA) which gives a canonical (unique) representation of the material properties. Numerical upscaling results are shown. The voxel microstructure of the two-phase composite material is extracted from a high resolution computed tomography image.
The dynamics of cluster growth in a two-lane driven diffusive system is analyzed by extensive Mon... more The dynamics of cluster growth in a two-lane driven diffusive system is analyzed by extensive Monte Carlo simulations. We observe good dynamical scaling for small values of a particle-particle exchange probability γ on relatively small lattices. As γ increases, the (effective) scaling exponents develop a dependence on γ, suggesting that the observed coarsening does not result in a genuine ordered
We deal with the solution of the systems of linear algebraic equations arising from Symmetric Int... more 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 piecewise linear discontinuous functions. The presented approach has recently been introduced in [2] in the context of designing subspace correction methods for scalar elliptic partial differential equations and is extended here to linear elasticity equations, i.e., a class of vector field problems. Similar to the scalar case the solution of the linear algebraic system corresponding to the SIPG method is reduced to the solution of a problem arising from discretization by nonconforming Crouzeix-Raviart elements plus the solution of a well-conditioned problem on the complementary space.
Grigorova, N., Zh. Ivanova, E. Dichlianova, T. Georgieva, T. Slavov, E. Vachkova & I. Penchev Geo... more Grigorova, N., Zh. Ivanova, E. Dichlianova, T. Georgieva, T. Slavov, E. Vachkova & I. Penchev Georgiev, 2015. The effect of antioxidant treatment on blood lactate and pyruvate concentrations in a rabbit model of obesity. Bulg. J. Vet. Med. (online first). In the current study, the impact of dietary antioxidant supplementation on fasting blood lactate and pyruvate concentrations in a rabbit model of obesity was investigated. A total of 26 rabbits were randomly divided into 3 groups: castrated and obese animals (CO, n=7); castrated, obese and treated with antioxidants (Immunoprotect, n=7, CIm) and non-castrated, non-treated controls (NC, n=12). At the end of the 2-month treatment period blood lactate concentration, lactate to pyruvate and lactate to glucose ratio in CIm were significantly (P<0.05) lower than in NC and tended to be lower than in CO. No group differences in pyruvate and glucose concentrations were found. There was a significant negative (r =–0.53; P<0.05) correlat...
ABSTRACT The structure of the honeycomb-like three-dimensional networks formed on self-assembly o... more ABSTRACT The structure of the honeycomb-like three-dimensional networks formed on self-assembly of the tetradentate ligand 1,2-bis(5′-dipyrimidyl)ethyne with copper (I) iodide and copper (I) bromide are presented.
We present precision Monte Carlo data and analytic arguments for an asymmetric exclusion process,... more We present precision Monte Carlo data and analytic arguments for an asymmetric exclusion process, involving two species of particles driven in opposite directions on a 2 × L lattice. We propose a scenario which resolves a stark discrepancy between earlier simulation data, suggesting the existence of an ordered phase, and an analytic conjecture according to which the system should revert to a disordered state in the thermodynamic limit. By analyzing the finite size effects in detail, we argue that the presence of a single, seemingly macroscopic, cluster is an intermediate stage of a complex nucleation process: In smaller systems, this cluster is destabilized while larger systems allow the formation of multiple clusters. Both limits lead to exponential cluster size distributions which are, however, controlled by very different length scales.
Journal of Physics A: Mathematical and General, 2006
Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening pheno... more Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening phenomena in a simple driven diffusive system. The model is reminiscent of vehicular traffic on a two-lane ring road. At sufficiently high density, the system develops jams (clusters) which coarsen with time. A key parameter is the passing probability, γ. For small values of γ, the growing clusters display dynamic scaling, with a growth exponent of 2/3. For larger values of γ, the growth exponent must be adjusted, suggesting the ordered (jammed) state is not a genuine phase but rather a finite size effect.
Uploads
Papers by Ivan Georgiev