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Ссылки по методам построения расчетных сеток

1. V.A. Garanzha, I.E. Kaporin. Regularization of the Barrier Variational Method // Computational mathematics and mathematical physics, 1999, 39 (9), 1426-1440. Pdf file.
2. V.A. Garanzha, V.N. Konshin, S.L. Lyons, D.V. Papavassiliou, G. Qin. Validation of non-Darcy well models using direct numerical simulation //
Numerical Treatment of Multiphase Flows in Porous Media, Springer, 2000, pp.156-169. Pdf file.
3. V.A. Garanzha. Barrier method for quasi-isometric grid generation // Computational mathematics and mathematical physics, 2000, 40 (11), 1617-1637. Pdf file.
4. Garanzha V.A. Barrier variational generation of quasi-isometric grids // Num. Linear Algebra Appl. 2001. V.8. 5. P.329-353.
5. Branets L.V., Garanzha V.A. Distortion measure for trilinear mapping. Application to 3-D grid generation // Num. Linear Algebra Appl. 2002. V.9. 6-7. P.511-526. Pdf file.
6. Garanzha V.A. Maximum norm optimization of quasi-isometric mappings // Num. Linear Algebra Appl. 2002. V.9 6-7. P.493-510. Pdf file.
7. V.A. Garanzha. Control of the metric properties of spatial mappings // Computational mathematics and mathematical physics, 2003, 43 (6), 782-792. Pdf file.
8. V.A. Garanzha, N.L. Zamarashkin. Three-dimensional quasi-isometric mappings as minimizers of a polyconvex functional // Computational mathematics and mathematical physics, 2003,  43 (6), 815-826. Pdf file
9. Garanzha V.A. Variational principles in grid generation and geometric modeling: theoretical justifications and open problems // Num. Linear Algebra Appl. 2004. V.11. P. 535-563. Pdf file.
10. Garanzha V.A., Kaporin I.E., Konshin I.N. Truncated Newton type solver with application to grid untangling problem // Num. Linear Algebra Appl. 2004. V.11, 5-6. P.525-533.
11. V.A. Garanzha. Existence and invertibility theorems for the problem of the variational construction of quasi-isometric mappings with free boundaries \\ Computational Mathematics and Mathematical Physics, 2005, 45:3, 465–475.
12. V.A. Garanzha, I.E. Kaporin. On the convergence of a gradient method for the minimization of functionals in finite deformation elasticity theory and for the minimization of barrier grid functionals \\ Computational Mathematics and Mathematical Physics, 2005, 45:8, 1400–1415. Pdf file.
13. Garanzha V.A. Quasi-isometric surface parameterization // Appl. Num. Math. 2005. V.55. 3. P.295-311. Pdf file.
14. V.A. Garanzha, A.I. Golikov, Y.G. Evtushenko, M.K. Nguen. Parallel implementation of Newton’s method for solving large-scale linear programs \\ Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 8, pp 1303–1317. Pdf file.
15. Garanzha V.A. Approximation of the curvature of Alexandrov surfaces using dual polyhedra // Rus. J. Numer. Analys. Modeling. 2009. V.24. 5. P.409-423.
16. Garanzha V.A. Discrete extrinsic curvatures and approximation of surfaces by polar polyhedra // Ж. вычисл. матем. и матем. физ. 2010. Т.50. 1. С.71-98. Pdf file
17. Garanzha V.A.Polyconvex potentials, invertible deformations, and thermodynamically consistent formulation of the nonlinear elasticity equations \\ Computational Mathematics and Mathematical Physics, 2010, Vol. 50, No. 9, pp. 1561–1587. Pdf file
18. Vladimir A. Garanzha and L. N. Kudryavtseva.  Generation of three-dimensional delaunay meshes from weakly structured and inconsistent data.Computational Mathematics and Mathematical Physics, 52(3):427–447, 2012. Pdf file
19. V.A. Garanzha, L.N. Kudryavtseva, and S.V. Utyuzhnikov. Variational method for untangling and optimization of spatial meshes. Journal of Computational and Applied Mathematics, 269:24 – 41, 2014. Pdf file
20. A. I. Belokrys-Fedotov, V. A. Garanzha,  L. N. Kudryavtseva,  Generation of Delaunay Meshes in Implicit Domains with Edge Sharpening \\
Computational Mathematics and Mathematical Physics, 2016, Vol. 56, No. 11, pp. 1901–1918. Proof
21. A. I. Belokrys-Fedotov, V. A. Garanzha,  L. N. Kudryavtseva, Delaunay meshing of implicit domains with boundary edge sharpening and sliver elimination. 2017, Mathematics and Computers in Simulation 147 (2018) 2–26 Pdf file
22. V.A. Garanzha, L.N. Kudryavtseva, Hyperelastic springback technique for construction of prismatic mesh layers. 26th International Meshing Roundtable, IMR26, 18-21 September 2017, Barcelona, Spain, Procedia Engineering 203 (2017) 401–413 Pdf file  Best technical paper award at IMR26

Ссылки по методам вычислительной линейной алгебры

Konshin, I., Kaporin, I., Nikitin, K., Vassilevski, Y. Parallel linear systems solution for multiphase flow problems in the INMOST framework. Proceedings of the 1st Russian Conference on Supercomputing - Supercomputing Days 2015, Moscow, Russia, September 28-29, 2015 (pp. 96-103).

Kaporin, I. E. E., Milyukova, O. Y. (2013). Optimization of the factorized preconditioners of conjugate gradient method for solving the linear algebraic systems with symmetric positive definite matrix. Preprints of the Keldysh Institute of Applied Mathematics, 13-17.

Kaporin, I. E. E. (2012). Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method. Computational Mathematics and Mathematical Physics, 52(2), 169-193.

Kaporin, I. (2010). Scaling, preconditioning, and superlinear convergence in GMRES-type iterations. In Matrix Methods: Theory, Algorithms And Applications: Dedicated to the Memory of Gene Golub (pp. 273-295).

Kaporin, I., Konshin, I. (2009). Load Balancing of Parallel Block Overlapped Incomplete Cholesky Preconditioning. In Parallel Computing Technologies (pp. 304-315). Springer Berlin Heidelberg.

Kaporin, I. E., Kon’shin, I. N. (2009). Post-filtering of IC2-factors for load balancing in parallel preconditioning. Computational Mathematics and Mathematical Physics, 49(6), 901-918.

Kaporin, I. (2008). Multilevel ILU preconditionings for general unsymmetric matrices. In Proc. Int. Conf. NUMGRID/VORONOI-2008, Moscow (pp. 150-157).

Kaporin, I. E. (2008). Localization of the eigenvalues of a pencil of positive definite matrices. Computational Mathematics and Mathematical Physics, 48(11), 1917-1926.

Kaporin, I. E. (2007). Scaling, reordering, and diagonal pivoting in ILU preconditionings. Russian Journal of Numerical Analysis and Mathematical Modelling rnam, 22(4), 341-375.

Kaporin, I. (2005). Superlinear convergence in minimum residual iterations. Numerical linear algebra with applications, 12(5-6), 453-470.

Garanzha, V. A., Kaporin, I. E. (2005). On the convergence of a gradient method for the minimization of functionals in finite deformation elasticity theory and for the minimization of barrier grid functionals. Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 45(8), 1450-1465.

Kaporin, I. (2004). The aggregation and cancellation techniques as a practical tool for faster matrix multiplication. Theoretical Computer Science, 315(2), 469-510.

Garanzha, V., Kaporin, I., Konshin, I. (2004). Truncated Newton type solver with application to grid untangling problem. Numerical Linear Algebra with Applications, 11(5-6), 525-533.

Kaporin, I. E. E. (2003). Applications of the internal iterations of the conjugate gradients method to solution large scale sparse non-linear optimization problems. Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 43(6), 802-807.

Kaporin, I. E. (2003). Using inner conjugate gradient iterations in solving large-scale sparse nonlinear optimization problems. Computational mathematics and mathematical physics, 43(6), 766-771.

Kaporin, I. E. (2002). Using the modified 2nd order incomplete Cholesky decomposition as the conjugate gradient preconditioning. Numerical linear algebra with applications, 9(6-7), 401-408.

Kaporin, I. E., Konshin, I. N. (2002). A parallel block overlap preconditioning with inexact submatrix inversion for linear elasticity problems. Numerical linear algebra with applications, 9(2), 141-162.

Axelsson, O., Kaporin, I. (2001). Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations. Numerical Linear Algebra with Applications, 8(4), 265-286.

Kaporin, I. E., Kon'shin, I. N. (2001). Parallel solution of symmetric positive definite systems based on decomposition into overlapping blocks. Computational mathematics and mathematical physics, 41(4), 481-493.

Axelsson, O., Kaporin, I. (2001). Optimizing two-level preconditionings for the conjugate gradient method (pp. 3-21). Springer Berlin Heidelberg.

Axelsson, O., Kaporin, I. (2000). On the sublinear and superlinear rate of convergence of conjugate gradient methods. Numerical Algorithms, 25(1-4), 1-22.

Axelsson, O., Kaporin, I., Konshin, I., Kucherov, A., Neytcheva, M., Polman, B., Yeremin, A. (2000). Comparison of algebraic solution methods on a set of benchmark problems in linear elasticity. Final Report of the STW project NNS, 4683.

Yeremin, A. Y., Kaporin, I. E. (2000). The influence of isolated largest eigenvalues on the numerical convergence of the CG method. Journal of Mathematical Sciences, 101(4), 3231-3236.

Axelsson, O., Kaporin, I. (2000). A survey of Newton type methods for solving nonlinear boundary value problems. Hellenic European Research on Mathematics and Informatics Science, HERMIS–\mu\pi, 1, 93-108.

Garanzha, V. A., Kaporin, I. E. (1999). Regularization of the barrier variational method of grid generation. Computational mathematics and mathematical physics, 39(9), 1426-1440.

Kaporin, I. E., Konshin, I. N. (1999). Parallel solution of large sparse SPD linear systems based on overlapping domain decomposition. In Parallel Computing Technologies (pp. 436-446). Springer Berlin Heidelberg.

Kaporin, I. E. (1998). High quality preconditioning of a general symmetric positive definite matrix based on its UTU+UTR+RTU-decomposition. Numerical linear algebra with applications, 5(6), 483-509.

Garanzha, V. A., Kaporin, I. E., Konshin, V. N. (1998). Reliable flow solver based on the high order control volume Pade-type differences. In Sixteenth International Conference on Numerical Methods in Fluid Dynamics (pp. 278-283). Springer Berlin Heidelberg.

Kaporin, I. E., Axelsson, O. (1995). On a class of nonlinear equation solvers based on the residual norm reduction over a sequence of affine subspaces. SIAM Journal on Scientific Computing, 16(1), 228-249.

Axelsson, O., Kaporin, I. E. (1995). On the solution of nonlinear equations for nondifferentiable mappings (pp. 38-51). Vieweg+Teubner Verlag.

Kaporin, I. E. (1994). New convergence results and preconditioning strategies for the conjugate gradient method. Numerical linear algebra with applications, 1(2), 179-210.

Kaporin, I. E. (1994). Optimization of conjugate gradient algorithms. Computational Mathematics and Modeling, 5(2), 139-147.

Gushchin, I. S., Kaporin, I. E. (1994). Application of direct methods to solve difference problems of gas-discharge physics. Computational Mathematics and Modeling, 5(2), 120-126.

Kaporin, I. (1993). Spectrum boundary estimation for two-side explicit preconditioning. Vestnik Mosk. Univ., ser.Math., 15, 28-42.

Kaporin, I. E. (1993). Iterative solution of systems of linear equations using incomplete inverse triangular factorization. Computational Mathematics and Modeling, 4(1), 28-32.

Kaporin, I. E. (1992). Explicitly preconditioned conjugate gradient method for the solution of unsymmetric linear systems. International journal of computer mathematics, 44(1-4), 169-187.

Kaporin, I. E. (1992). Two-level explicit preconditioning of conjugate gradient method. Differential Equations, 28(2), 280-289.

Kaporin, I. E., Kolotilina, L. Y., Yeremin, A. Y. (1991). Block SSOR preconditionings for high-order 3D FE systems. II. Incomplete BSSOR preconditionings. Linear algebra and its applications, 154-156, 647-674.

Kaporin, I. E. (1991). Minimal iteration methods utilizing the generalized Krylov basis. Computational Mathematics and Modeling, 2(1), 10-16.

Kaporin, I. E. (1990). A preconditioned conjugate-gradient method for solving discrete analogs of differential problems. Differential Equations, 26(7), 897-906.

Kaporin, I. E. (1990). An alternative approach to estimating the convergence rate of the CG method. Numerical Methods and Software, Yu. A. Kuznetsov, ed., Dept. of Numerical Mathematics, USSR Academy of Sciences, Moscow, 55-72.

Yeremin, A. Y., Kaporin, I. E. E., & Kerimov, M. K. (1988). Computation of the derivatives of the Riemann zeta-function in the complex domain. USSR Computational Mathematics and Mathematical Physics, 28(4), 115-124.

Eremin, A. Y., Kaporin, I. E. (1987). Spectral optimization of explicit iterative methods. I. Journal of Soviet Mathematics, 36(2), 207-214.

Gasanov, A. I., Kaporin, I. E. (1986). Application of the elimination method in the solution of strongly elliptic systems by the finite element method. Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 26(6), 837-850.

Eremin, A. Y., Kaporin, I. E., Kerimov, M. K. (1985). The calculation of the Riemann zeta-function in the complex domain. USSR Computational Mathematics and Mathematical Physics, 25(2), 111-119.

Yeremin, A. Y., Kaporin, I. E., Kerimov, M. K. (1985). Calculation of the Riemann zeta function in a complex domain. Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 25(4), 500-511.

Yeremin, A. Y., Kaporin, I. E. (1984). Spectral optimization of explicit iterative methods. I. Chislennye Metody i Voprosy Organizatsii Vychislenii 7. Zapiski Nauchnykh Seminarov POMI, 139, 51-60.

Samarskii, A. A., Kaporin, I. E., Kucherov, A. B., Nikolaev, E. S. (1983). Some modern methods of solution of difference equations. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, (7), 3-12.

Kaporin, I. E., Nikolaev, E. S. (1983). Artificial unknown conjugate-direction method for finite difference elliptic problems with variable coefficients. Differential Equat., 18(7), 842-846.

Kaporin, I., Nikolaev, E. (1982). Complete reduction method for a set of special 3-point vector equations. Doklady Akademii Nauk SSSR, 264(5), 1056-1059.

Kaporin, I. E. (1982). A marching method for system with a block-tridiagonal matrix. In Numerical Methods of Linear Algebra (pp. 63-72). Izd. MGU Moscow.

Kaporin, I. E. (1980). Modified Marching Algorithm for Solving Difference Equations Approximating Dirichlet Problem for Poisson Equation in a Rectangular. In Difference Methods for Mathematical Physics Problems (p. 11).

Kaporin, I. E. (1980). A new fast Fourier transform algorithm. USSR Computational Mathematics and Mathematical Physics, 20(4), 253-259.

Kaporin, I. E., Nikolaev, E. S. (1980). The method of fictitious unknowns for solving difference elliptic equations in irregular domains. Differents. Uravn., 16(7), 1211-1225.

Kaporin, I. E., Nikolaev, E. S. (1980). Fictitious-Variable Method for the Solution of Elliptic Finite-Difference Boundary-Value Problems in Irregular Regions. Differential Equat., 16(7), 756-767.

Kaporin, I. E., Nikolaev, E. S. (1980). The method of fictitious unknowns for solving equations of elliptic type in domains of complex shape. In Dokl. Akad. Nauk SSSR (Vol. 251, No. 3, pp. 544-548).