Discussion of ‘Motives for disclosure and nondisclosure: a review of the evidence’

We develop a new high order accurate time-integration technique for initial value problems. We focus on problems that originate from a space approximation using high order finite difference methods on summation-by-parts form with weak boundary conditions, and extend that technique to the time-domain. The new time-integration method is global, high order accurate, unconditionally stable and together with the approximation in space, it generates optimally sharp fully discrete energy estimates. In particular, it is shown how stable fully discrete high order accurate approximations of the Maxwells’ equations, the elastic wave equations and the linearized Euler and Navier-Stokes equations can obtained. Even though we focus on finite difference approximations, we stress that the methodology is completely general and suitable for all semi-discrete energy-stable approximations. Numerical experiments show that the new technique is very accurate and has limited order reduction for stiff problems

Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes

We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable coefficient initial boundary value problems can be formulated in simple and straightforward ways using high-order accurate operators of generalized summation-by-parts type. Encapsulated features on a single computational block or element may include polynomial bases, tensor products as well as curvilinear coordinate transformations. Moreover, through the use of inner product preserving interpolation or projection, the global summation-by-parts property in extended to arbitrary multi-block or multi-element meshes with non-conforming nodal interfaces

Summation-By-Parts Operators for Time Discretisation: Initial Investigations

Abstract We develop a new high order accurate time-discretisation technique for initial value problems. We focus on problems that originate from a space discretisation using high order finite difference methods on summation-by-parts form with weak boundary conditions, and extend that technique to the time-domain. The new timediscretisation method is global and together with the approximation in space, it generates optimal fully discrete energy estimates, and efficient methods for both stiff and non-stiff problems. In particular, it is shown how stable fully discrete high order accurate approximations of the Maxwells' equations, the elastic wave equations and the linearised Euler and Navier-Stokes equations are obtained. Even though we focus on finite difference approximations, we stress that the methodology is completely general and suitable for all semi-discrete energy-stable approximations

Stability of SBP schemes on overlapping domains

Using fnite difference methods for partial differential equations, this thesis focuses on the problem of connecting overlapping solution domains in the context of a frst order hyperbolic problem. Especially the stability properties of such constructions is studied, and a stable general implementation of the the test problem is proposed. However, no energy estimate could be found, and indeed proven not to exist in the natural norm. Finally, an example is also put forward where the interface conditions derived are, for stability considerations, incompatible with the boundary conditions in a coupled system of hyperbolic equations

FEM-modelling of SSRT for Corrosion Tests

This thesis discusses the mathematical formulation and computational treatment of slow strain rate corrosion tests based on nonlinear finite elements methods. The theory is illustrated by a description of classical small strain elastoplasticity theory as implemented in the Comsol Multiphysics 3.2 software package. The possible extension of the theory to finite strain is briefly addressed. Practical simulations and results regarding the evolution of stresses, strains and geometric deformation are also presented and discussed. Experimental data used in simulation where reported by Onchi, Takeo et al. and published in Journal of Nuclear Science and Technology in May 2006

High order summation-by-parts methods in time and space

This thesis develops the methodology for solving initial boundary value problems with the use of summation-by-parts discretizations. The combination of high orders of accuracy and a systematic approach to construct provably stable boundary and interface procedures makes this methodology especially suitable for scientific computations with high demands on efficiency and robustness. Most classes of high order methods can be applied in a way that satisfies a summation-by-parts rule. These include, but are not limited to, finite difference, spectral and nodal discontinuous Galerkin methods. In the first part of this thesis, the summation-by-parts methodology is extended to the time domain, enabling fully discrete formulations with superior stability properties. The resulting time discretization technique is closely related to fully implicit Runge-Kutta methods, and may alternatively be formulated as either a global method or as a family of multi-stage methods. Both first and second order derivatives in time are considered. In the latter case also including mixed initial and boundary conditions (i.e. conditions involving derivatives in both space and time). The second part of the thesis deals with summation-by-parts discretizations on multi-block and hybrid meshes. A new formulation of general multi-block couplings in several dimensions is presented and analyzed. It collects all multi-block, multi-element and  hybrid summation-by-parts schemes into a single compact framework. The new framework includes a generalized description of non-conforming interfaces based on so called summation-by-parts preserving interpolation operators, for which a new theoretical accuracy result is presented

On the Suboptimal Accuracy of Summation-by-parts Schemes with Non-conforming Block Interfaces

We derive a bound on the formal accuracy of interpolation schemes for energy stable summation-by-parts discretizations on non-conforming multiblock grids. This result explains the suboptimal accuracy for such schemes reported in previous works. Numerical simulations confirm a corresponding reduced convergence rate in both maximum and L2 norms

Author Subjectivity in the Descriptions of Politicians’ Lives (comparative linguistic analysis of texts by Plutarch and Svetonius)

Maģistra darba nolūks ir analizēt subjektivitātes izteikšanas līdzekļus Plūtarha Βίοι Παράλληλοι un Svētonija De vita Caesarum ar mērķi izpētīt un salīdzināt tās Plūtarha un Svētonija tekstos, izvērtējot to saturu un lomu. Teorētiskajā daļā aplūkota zinātniska literatūra par Plūtarha un Svētonija stila, Βίοι Παράλληλοι un Svetonija De vita Caesarum vispārīgo raksturojumu un subjektivitātes jēdziena nozīmi. Praktiskā daļa ir balstīta uz analīzi, kas veikta ar subjektivitātes piemēriem tekstā, galvenokārt izmantojot kontekstuālu analīzi. Pētījuma objekts ir trīs Plūtarha un attiecīgi trīs Svētonija biogrāfiju teksti (Otons, Galba, Cēzars). Subjektivitātes piemēri tiek klasificēti pēc to izpausmes tekstā: tieši - no autora vārdiem - un netiešā veidā, kad autora subjektīvais viedoklis redzams citu cilvēku teiktajā. Darbā tiek salīdzinātas subjektivitātes izpausmes un biežums Plūtarha un Svētonija tekstos. Secināts, ka subjektivitāte biežāk parādās Svētonija tekstos, nevis Plūtarha darbos. Svētonija subjektivitāte biežāk izpaužas valodas līmenī, Plūtarha subjektivitātē paradās domu līmenī.Master's thesis is intended to analyze the expression of subjectivity in Plutarch Βίοι Παράλληλοι and in Suetonius De vita Caesar with the aim to study and compare Plutarch and Suetonius texts, evaluating their content and role. In the theoretical part of the paper was viewed the scientific literature about Plutarch and Suetonius style, Βίοι Παράλληλοι and Suetonius De vita Caesars general characteristics and importance of the concept of subjectivity. The practical part is based on the analysis which is made with subjective examples in the text, mainly used contextual analysis. The subject of the research is three Plutarch and three Suetonius biographies text (Otons, Galba, Caesar). Examples of subjectivity are classified according to their expression in the text: directly - from the author's words - and indirectly, when the author's subjective opinion is seen in the words of other people. The paper compares the manifestations and frequency of subjectivity in the texts of Plutarch and Suetonius. It is concluded that subjectivity appears more often in the texts of Suetonius than in the works of Plutarch. Suetonius subjectivity more often manifests itself at the linguistic level, and Plutarch's subjectivity prevails at the thought level

Summation-by-parts in Time: the Second Derivative

A new technique for time integration of initial value problems involving second derivatives is presented. The technique is based on summation-by-parts operators and weak initial conditions and lead to optimally sharp energy estimates. The schemes obtained in this way use wide operators, are unconditionally stable and high order accurate. The additional complications when using compact operators in time are discussed in detail and it is concluded that the existing compact formulations designed for space approximations are not appropriate. As an application we focus on the wave equation and derive optimal fully discrete energy estimates which lead to unconditional stability. The scheme utilizes wide stencil operators in time, whereas the spatial operators can have both wide and compact stencils. Numerical calculations verify the stability and accuracy of the new methodology

Stable and Accurate Filtering Procedures

High frequency errors are always present in numerical simulations since no difference stencil is accurate in the vicinity of the $$\pi$$π-mode. To remove the defective high wave number information from the solution, artificial dissipation operators or filter operators may be applied. Since stability is our main concern, we are interested in schemes on summation-by-parts (SBP) form with weak imposition of boundary conditions. Artificial dissipation operators preserving the accuracy and energy stability of SBP schemes are available. However, for filtering procedures it was recently shown that stability problems may occur, even for originally energy stable (in the absence of filtering) SBP based schemes. More precisely, it was shown that even the sharpest possible energy bound becomes very weak as the number of filtrations grow. This suggest that successful filtering include a delicate balance between the need to remove high frequency oscillations (filter often) and the need to avoid possible growth (filter seldom). We will discuss this problem and propose a remedy.Funding agencies:  Linkoping University</p