Pekka Neittaanmäki

A parallel splitting up method and its application to Navier-Stokes equations

Abstract A parallel splitting-up method (or the so called alternating-direction method) is proposed in this paper. The method not only reduces the original linear and nonlinear problems into a series of one dimensional linear problems, but also enables us to compute all these one dimensional linear problems by parallel processors. Applications of the method to linear parabolic problem, steady state and nonsteady state Navier-Stokes problems are given.

Superconvergence phenomenon in the finite element method arising from averaging gradients

SummaryWe study a superconvergence phenomenon which can be obtained when solving a 2nd order elliptic problem by the usual linear elements. The averaged gradient is a piecewise linear continuous vector field, the value of which at any nodal point is an average of gradients of linear elements on triangles incident with this nodal point. The convergence rate of the averaged gradient to an exact gradient in theL2-norm can locally be higher even by one than that of the original piecewise constant discrete gradient.

Simulation model for improving the operation of the emergency department of special health care

This paper presents a simulation model which describes the operations in the Emergency Department of Special Health Care at the Central Hospital of Jyvaskyla, Finland. It can be used to test different process scenarios, allocate resources and perform activity based cost analysis. By using the simulation model we demonstrate a new operational method, which makes the operation of the Emergency Department of Special Health Care more effective. This operational method is called the triage-team method and it has been studied from two different points of view. The results showed that this method improves the operation of the Emergency Department of Special Health Care substantially (over 25%), if it is implemented properly and includes all the necessary tasks

On a global superconvergence of the gradient of linear triangular elements

Abstract We study a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements. The recovered gradient globally approximates the true gradient even by one order of accuracy higher in the L 2 -norm than the piecewise constant gradient of the Ritz—Galerkin solution. A superconvergent approximation to the boundary flux is presented as well.

Mathematical and numerical modelling in electrical engineering theory and applications

Glossary of Symbols. Foreword. 1. Introduction. 2. Mathematical Modelling of Physical Phenomena. 3. Mathematical Background. 4. Finite Elements. 5. Conjugate Gradients. 6. Magnetic Potential of Transformer Window. 7. Calculation of Nonlinear Stationary Magnetic Fields. 8. Steady-State Radiation Heat Transfer Problem. 9. Nonlinear Anisotropic Heat Conduction in a Transformer Magnetic Core. 10. Stationary Semiconductor Equations. 11. Nonstationary Heat Conduction in a Stator. 12. The Time-Harmonic Maxwell Equations. 13. Approximation of the Maxwell Equations in Anisotropic Inhomogeneous Media. 14. Methods for Optimal Shape Design of Electrical Devices. References. Author index. Subject index.

Variational and Quasi-Variational Inequalities in Mechanics

1. Notation and Basics: 1.1. Notations and Conventions 1.2. Functional spaces 1.3. Bases and complete systems. Existence theorem 1.4. Trace Theorem 1.5. The laws of thermodynamics 2. Variational Setting of Linear Steady-state Problems: 2.1. Problem of the equilibrium of system with a finite number of degrees of Freedom 2.2. Equilibrium of the simplest continuous systems governed by ordinary differential Equations 2.3. 3D and 2D problems on the equilibrium of linear elastic bodies 3.4. Positive definiteness of the potential energy of linear systems 3.Variational Theory for Nonlinear Smooth Systems: 3.1. Examples of nonlinear systems 3.2. Differentiation of operators and functionals 3.3. Existence and uniqueness theorems of the minimal point of a functional 3.4. Condition for the potentiality of an operator 3.5. Boundary value problems in the Hencky-Ilyushin theory of plasticity without discharge 3.6. Problems in the elastic bodies theory with finite displacements and strain 4. Unilateral Constraints and Non-Differentiable Functionals: 4.1. Introduction: systems with finite degrees of freedom 4.2. Variational methods in contact problems for deformed bodies without friction 4.3. Variational method in contact problem with friction 5. The Transformation of Variational Principles: 5.1. Friedrichs Transformation 5.2. Equilibrium, mixed and hybrid variational principles in the theory of elasticity 5.3. The Young-Fenchel-Moreau duality transformation 5.4. Applications of duality transformations in contact problems 6. Non-Stationary Problems and Thermodynamics: 6.1. Traditional principles and methods 6.2. Gurtins method 6.3. Thermodynamics and mechanics of the deformed solids 6.4. The variational theory of adhesion and crack initiation 7. Solution Methods and Numerical implementation: 7.1. Frictionless contact problems: finite element method (FEM) 7.2. Friction contact problems: boundaryelement method (BEM) 8. Concluding Remarks: 8.1. Modelling. Identification problem. Optimization 8.2. Development of the contact problems with friction, wear and adhesion 8.3. Numerical implementation of the contact interaction phenomena References Index.

Mathematical Models in Electrical Circuits: Theory and Applications

I. Dissipative operators and differential equations on Banach spaces.- 1.0. Introduction.- 1.1. Duality type functionals.- 1.2. Dissipative operators.- 1.3. Semigroups of linear operators.- 1.4. Linear differential equations on Banach spaces.- 1.5. Nonlinear differential equations on Banach spaces.- II. Lumped parameter approach of nonlinear networks with transistors.- 2.0. Introduction.- 2.1. Mathematical model.- 2.2. Dissipativity.- 2.3. DC equations.- 2.4. Dynamic behaviour.- 2.5. An example.- III. lp-solutions of countable infinite systems of equations and applications to electrical circuits.- 3.0. Introduction.- 3.1. Statement of the problem and preliminary results.- 3.2. Properties of continuous lp-solutions.- 3.3. Existence of continuous lp-solutions for the quasiautonomous case.- 3.4. Truncation errors in linear case.- 3.5. Applications to infinite circuits.- IV. Mixed-type circuits with distributed and lumped parameters as correct models for integrated structures.- 4.0. Why mixed-type circuits?.- 4.1. Examples.- 4.2. Statement of the problem.- 4.3. Existence and uniqueness for dynamic system.- 4.4. The steady state problem.- 4.5. Other qualitative results.- 4.6. Bibliographical comments.- V. Asymptotic behaviour of mixed-type circuits. Delay time predicting.- 5.0. Introduction.- 5.1. Remarks on delay time evaluation.- 5.2. Asymptotic stability. Upper bound of delay time.- 5.3. A nonlinear mixed-type circuit.- 5.4. Comments.- VI. Numerical approximation of mixed models for digital integrated circuits.- 6.0. Introduction.- 6.1. The mathematical model.- 6.2. Construction of the system of FEM-equations.- 6.2.1. Space discretization of reg-lines.- 6.2.2. FEM-equations of lines.- 6.3. FEM-equations of the model.- 6.4. Residual evaluations.- 6.5. Steady state.- 6.6. The delay time and its a-priori upper bound.- 6.7. Examples.- 6.8. Concluding remarks.- Appendix I.- List of symbols.- References.

Fixed domain approaches in shape optimization problems

This work is a review of results in the approximation of optimal design problems, defined in variable/unknown domains, based on associated optimization problems defined in a fixed ?hold-all? domain, including the family of all admissible open sets. The literature in this respect is very rich and we concentrate on three main approaches: penalization?regularization, finite element discretization on a fixed grid, controllability and control properties of elliptic systems. Comparison with other fixed domain approaches or, in general, with other methods in shape optimization is performed as well and several numerical examples are included.

Second-order optimality conditions for nondominated solutions of multiobjective programming with

We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion function as well as constraint functions are supposed to be from the class C1,1. Second-order optimality conditions for local Pareto solutions are derived as a special case.

C^{1,1}

In this paper a steady-state nonlinear parabolic-type model, which simulates the multiphase heat transfer during solidification in continuous casting, is presented. An enthalpy formulation is used and we apply a FE-method in space and an implicit Euler method in time. A detailed solution algorithm is presented. We compute the temperature distributions in the strand when the boundary conditions (mold/spray cooling) on the strand surface are known. The numerical model gives thereby a good basis for the testing of new designs of continuous-casting machines. An application of the model to continuous casting of billets is presented.