Yavor Vutov

Finite volume discretization of equations describing nonlinear diffusion in Li-Ion batteries

Numerical modeling of electrochemical process in Li-Ion battery is an emerging topic of great practical interest. In this work we present a Finite Volume discretization of electrochemical diffusive processes occurring during the operation of Li-Ion batteries. The system of equations is a nonlinear, time-dependent diffusive system, coupling the Li concentration and the electric potential. The system is formulated at length-scale at which two different types of domains are distinguished, one for the electrolyte and one for the active solid particles in the electrode. The domains can be of highly irregular shape, with electrolyte occupying the pore space of a porous electrode. The material parameters in each domain differ by several orders of magnitude and can be nonlinear functions of Li ions concentration and/or the electrical potential. Moreover, special interface conditions are imposed at the boundary separating the electrolyte from the active solid particles. The field variables are discontinuous across such an interface and the coupling is highly nonlinear, rendering direct iteration methods ineffective for such problems. We formulate a Newton iteration for a purely implicit Finite Volume discretization of the coupled system. A series of numerical examples are presented for different type of electrolyte/electrode configurations and material parameters. The convergence of the Newton method is characterized both as function of nonlinear material parameters and the nonlinearity in the interface conditions.

Parallel MIC(0) preconditioning of 3D elliptic problems discretized by Rannacher-Turek finite elements

Novel parallel algorithms for the solution of large FEM linear systems arising from second order elliptic partial differential equations in 3D are presented. The problem is discretized by rotated trilinear nonconforming Rannacher-Turek finite elements. The resulting symmetric positive definite system of equations Ax=f is solved by the preconditioned conjugate gradient algorithm. The preconditioners employed are obtained by the modified incomplete Cholesky factorization MIC(0) of two kinds of auxiliary matrices B that both are constructed as locally optimal approximations of A in the class of M-matrices. Uniform estimates for the condition number @k(B^-^1A) are derived. Two parallel algorithms based on the different block structures of the related matrices B are studied. The numerical tests confirm theory in that the algorithm scales as O(N^7^/^6) in the matrix order N.

On the Pore-Scale Modeling and Simulation of Reactive Transport in 3D Geometries

Pore-scale modeling and simulation of reactive flow in porous media has a range of diverse applications, and poses a number of research challenges. It is known that the morphology of a porous medium has significant influence on the local flow rate, which can have a substantial impact on the rate of chemical reactions. While there are a large number of papers and software tools dedicated to simulating either fluid flow in 3D computerized tomography (CT) images or reactive flow using pore-network models, little attention to date has been focused on the pore-scale simulation of sorptive transport in 3D CT images, which is the specific focus of this paper. Here we first present an algorithm for the simulation of such reactive flows directly on images, which is implemented in a sophisticated software package. We then use this software to present numerical results in two resolved geometries, illustrating the importance of pore-scale simulation and the flexibility of our software package.

Supervised 2-Phase Segmentation of Porous Media with Known Porosity

Porous media segmentation is a nontrivial and often quite inaccurate process, due to the highly irregular structure of the segmentation phases and the huge interaction among them. 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.

Optimal solvers for linear systems with fractional powers of sparse SPD matrices: Optimal Solvers for Linear Systems with Fractional Powers of Sparse SPD Matrices

In this paper we consider efficient algorithms for solving the algebraic equation

Comparison of Two Techniques for Radio‐frequency Hepatic Tumor Ablation through Numerical Simulation

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Parallel DD-MIC(0) Preconditioning of Nonconforming Rotated Trilinear FEM Elasticity Systems

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Parallel MIC(0) preconditioning for numerical upscaling of anisotropic linear elastic materials

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Computer Simulation of RF Liver Ablation on an MRI Scan Data

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Balancing the communications and computations in parallel FEM simulations on unstructured grids

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