Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

During the last decade, a big progress has been achieved in the analysis and numerical treatment of Initial Value Problems (IVPs) in Differential Algebraic Equations (DAEs) and Ordinary Differential Equations (ODEs). In spite of the rich variety of results available in the literature, there are still many specific problems that require special attention. Two of such, which are considered in this work, are the optimization of order of accuracy and reduction of cost of functional evaluations of Explicit Runge - Kutta (ERK) methods.

Traditionally, the maximum attainable order p of an s-stage ERK method for advancing the solution of an IVP is such that
p(s)
 4
 
In 1999, Goeken presented an s-stage ERK Method of order p(s)=s +1,s>2.
However, this work focuses on the design of a new approximation algorithm that reduces the cost of functional evaluations and yet increases the attainable order higher 
U n and Jonhson [94]; and the classical ERK methods. The order p of 
the new scheme called Multiderivative Explicit Runge-Kutta (MERK) Methods is such that p(s) 2. The stability, convergence and implementation for the optimization of IVPs in DAEs and ODEs systems are also considered.

Numerical solution of initial value problems in differential - algebraic equations

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics)

The Physics of Rubber Elasticity (J. Meixner)

https://hal.archives-ouvertes.fr/hal-00457010/document

B¯ and F¯ projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements

Within the framework of finite elements the linearization within a Newton-like method requires the computation of the so-called consistent tangent operator There are several possibilities to get these derivatives Three methods, namely analytical, numerical and automatic differentiation, for tangent generation will be analyzed concerning the simulation time and applicability for three different constitutive models These models are a finite strain hyperelasticity model, finite strain viscoplasticity model for metal powders and a small strain thermoviscoplasticity model (© 2012 Wiley-VCH Verlag GmbH & Co KGaA, Weinheim)

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.201210146

Accelerating constitutive modeling by automatic tangent generation

Article Alexander Werth. 2021. Morphosyntax und Pragmatik in Konkurrenz. Der Definitartikel bei Personennamen in den regionalen und historischen Varietäten des Deutschen (Studia Linguistica Germanica 136). Berlin, Boston: De Gruyter. 465 S. was published on December 1, 2022 in the journal Zeitschrift für Rezensionen zur germanistischen Sprachwissenschaft (volume 14, issue 1-2). 

Alexander Werth. 2021. Morphosyntax und Pragmatik in Konkurrenz. Der Definitartikel bei Personennamen in den regionalen und historischen Varietäten des Deutschen (Studia Linguistica Germanica 136). Berlin, Boston: De Gruyter. 465 S.

Modeling and Simulation of the Thickness Dependence in Die Casting Structures

In isothermal solid mechanics, the space and time domain need to be discretized. This paper presents an approach using high-order finite elements based on Legendre polynomials for the spatial discretization and time-adaptive diagonal-implicit Runge-Kutta methods for the temporal discretization. The superiority of this approach over a traditional one using linear shape functions for the space domain and a Backward-Euler scheme for the time domain is demonstrated.

https://www.researchgate.net/profile/Stefan_Hartmann4/publication/264365683_High-Order_Time_Integration_in_the_p-Version_of_Finite_Elements/links/540b57e10cf2f2b29a31939a.pdf

High-Order Time Integration in the p-Version of Finite Elements

We consider the coupling of the compressible Navier‐Stokes equations with the heat equation as a model for cooling processes in steel forming. The semidiscrete coupled system is solved using stiffly stable SDIRK methods of higher order, where on each stage, a fluid‐structure interaction problem is solved.

Stefan Hartmann

Papers

Accelerating constitutive modeling by automatic tangent generation

Alexander Werth. 2021. Morphosyntax und Pragmatik in Konkurrenz. Der Definitartikel bei Personennamen in den regionalen und historischen Varietäten des Deutschen (Studia Linguistica Germanica 136). Berlin, Boston: De Gruyter. 465 S.

Modeling and Simulation of the Thickness Dependence in Die Casting Structures

High-Order Time Integration in the p-Version of Finite Elements

On Higher Order Time Integration for Thermal Coupling