One of the current main challenges in the area of scientific computing is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented. Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.

One of the current main challenges in the area of scientific computing is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented. Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.

This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on Large-Scale Scientific Computations, LSSC 2011, held in Sozopol, Bulgaria, in June 2011. The 74 revised full papers presented together with 3 plenary and invited papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on robust multigrid, multilevel and multiscale, deterministic and stochastic methods for modeling highly heterogeneous media, advanced methods for transport, control and uncertain systems, applications of metaheuristics to large-scale problems, environmental modelling, large scale computing on many-core architectures, multiscale industrial, enviromental and biomedical problems, efficient algorithms of computational geometry, high performance Monte Carlo simulations, voxel based computations and contributed papers.

This book constitutes the thoroughly refereed post-conference proceedings of the 4th International Conference on Numerical Analysis and Its Applications, NAA 2008, held in Lozenetz, Bulgaria in June 2008.

The 61 revised full papers presented together with 13 invited papers were carefully selected during two rounds of reviewing and improvement. The papers address all current aspects of numerical analysis and discuss a wide range of problems concerning recent achievements in physics, chemistry, engineering, and economics. A special focus is given to numerical approximation and computational geometry, numerical linear algebra and numerical solution of transcendental equations, numerical methods for differential equations, numerical modeling, and high performance scientific computing.

The 6th International Conference on Large-Scale Scienti?c Computations (LSSC 2007) was held in Sozopol, Bulgaria, June 5-9, 2007. The conference was organized by the Institute for Parallel Processing at the Bulgarian Academy of Sciences in cooperation with SIAM (Society for Industrial and Applied Ma- ematics). Partial support was also provided from project BIS-21++ funded by the European Commission in FP6 INCO via grant 016639/2005. The conference was devoted to the 60th anniversary of Richard E. Ewing. ProfessorEwingwasawardedthemedaloftheBulgarianAcademyofSciencesfor hiscontributionstotheBulgarianmathematicalcommunityandtotheAcademy ofSciences.Hiscareerspanned33years, primarilyinacademia, butalsoincluded industry. Since 1992 he worked at Texas A&M University being Dean of Science and Vice President of Research, as well as director of the Institute for Scienti?c Computation (ISC), which he founded in 1992. Professor Ewing is internati- ally well known with his contributions in applied mathematics, mathematical modeling, and large-scale scienti?c computations. He inspired a generation of researchers with creative enthusiasm for doing science on scienti?c compu- tions. The preparatorywork on this volume was almost done when the sad news came to us: Richard E. Ewing passed away on December 5, 2007 of an apparent heart attack while driving home from the o?ce.

Thepapersinthis volumewerepresentedatthe4thInternationalConferenceon Large-Scale Scienti?c Computations ICLSSC 2003. It was held in Sozopol, B- garia, June 4-8, 2003. The conference was organized and sponsored by the C- tral Laboratory for Parallel Processing at the Bulgarian Academy of Sciences. Support was also provided from the Center of Excellence "BIS 21" (funded by the European Commission), SIAM and GAMM. A co-organizer of this tra- tional scienti?c meeting was the Division of Numerical Analysis and Statistics of the University of Rousse. The success of the conference and the present volume in particular are the outcome of the joint e?orts of many colleagues from various institutions and organizations. First thanks to all the members of the Scienti?c Committee for their valuable contribution to forming the scienti?c face of the conference, as well as for their help in reviewing contributed papers. We would like to specially thank the organizers of the special sessions: R. Blaheta, N. Dimitrova, A. Ebel, K. Georgiev, O. Iliev, A. Karaivanova, H. Kosina, M. Krastanov, U. Langer, P. Minev, M. Neytcheva, M. Sch. afer, V. Veliov, and Z. Zlatev. We are also grateful to the sta? involved in the local organization. Special Events: - The conference was devoted to the 60th anniversary of Raytcho Lazarov. - During the conference, the nomination for the World Level of the Hall of Fame for Engineering, Science and Technology, HOFEST, was o?cially awarded to Owe Axelsson.

This book constitutes the thoroughly refereed post-proceedings of the 5th International Conference on Numerical Methods and Applications, NMA 2002, held in Borovets, Bulgaria, in August 2002. The 58 revised full papers presented together with 6 invited papers were carefully selected from numerous submissions during two rounds of reviewing and improvement. In accordance with various mini-symposia, the papers are organized in topical sections on Monte Carlo and Quasi-Monte Carlo methods, robust iterative solution methods and applications, control and uncertainty systems, numerical methods for sensor data processing, as well as in a section comprising various other methods, tools, and applications.

This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Large-Scale Scientific Computing, LSSC 2001, held in Sozopol, Bulgaria, in June 2001.The 7 invited full papers and 45 selected revised papers were carefully reviewed for inclusion in the book. The papers are organized in topical sections on robust preconditioning algorithms, Monte-Carlo methods, advanced programming environments for scientific computing, large-scale computations in air pollution modeling, large-scale computations in mechanical engineering, and numerical methods for incompressible flow.

This book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Large-Scale Scientific Computations, LSSC 2015, held in Sozopol, Bulgaria, in June 2015. The 49 revised full papers presented were carefully reviewed and selected from 64 submissions. The general theme for LSSC 2015 was Large-Scale Scientific Computing with a particular focus on the organized special sessions: enabling exascale computation; control and uncertain systems; computational microelectronics - from monte carlo to deterministic approaches; numerical methods for multiphysics problems; large-scale models: numerical methods, parallel computations and applications; mathematical modeling and analysis of PDEs describing physical problems; a posteriori error control and iterative methods for maxwell type problems; efficient algorithms for hybrid HPC systems; multilevel methods on graphs; and applications of metaheuristics to large-scale problems.