Related papers: Calculation of multi-scale, multi-loop integrals u…
We introduce three related but distinct improvements to multilevel Monte Carlo (MLMC) methods for the solution of systems of stochastic differential equations (SDEs). Firstly, we show that when the payoff function is twice continuously…
We present version 3 of Kira, a Feynman integral reduction program for high-precision calculations in quantum field theory and gravitational-wave physics. Building on previous versions, Kira 3 introduces optimized seeding and equation…
The sheet current model underlying the software 3D-MLSI package for calculation of inductances of multilayer superconducting circuits, has been further elaborated. The developed approach permits to overcome serious limitations on the shape…
Many applications in computational physics that use numerical integrators based on splitting and composition can benefit from the development of optimized algorithms and from choosing the best ordering of terms. The cost in programming and…
In this paper we develop further and refine the method of differential equations for computing Feynman integrals. In particular, we show that an additional iterative structure emerges for finite loop integrals. As a concrete non-trivial…
A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass…
We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…
We present the version 2.0 of the program GoSam, which is a public program package to compute one-loop corrections to multi-particle processes. The extended version of the "Binoth-Les-Houches-Accord" interface to Monte Carlo programs is…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructing substructures of wreath products, the so called cascade…
Stochastic differential equations (SDEs) are widely used to model systems affected by random processes. In general, the analysis of an SDE model requires numerical solutions to be generated many times over multiple parameter combinations.…
In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…
This paper summarizes my doctoral research on evaluation algorithms for HEX-programs, which extend Answer Set Programming with means for interfacing external computations. The focus is on integrating different subprocesses of…
We present here Multem 3, an updated and revised version of Multem 2, which syntax has been upgraded to Fortran 2018, with the source code being divided into modules. Multem 3 is equipped with LAPACK, the state-of-the art Faddeeva complex…
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the…
The calculation and manipulation of large multi-variable rational functions is a key bottleneck in multi-loop calculations. In these conference proceedings, based on my article [Chawdhry (2023) arXiv:2312.03672], I present a technique to…
In this note we report on the new version of FeynCalc, a Mathematica package for symbolic semi-automatic evaluation of Feynman diagrams and algebraic expressions in quantum field theory. The main features of version 9.0 are: improved tensor…
We propose a method for computing numerically integrals defined via $i \epsilon$ deformations acting on single-pole singularities. We achieve this without an explicit analytic contour deformation. Our solution is then used to produce…
Students of our department solve algebraic exercises in mathematical logic in a computerized environment. They construct transformations step by step and the program checks the syntax, equivalence of expressions and completion of the task.…
Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly…