A New Method for the Calculation of Functional and Path Integrals

by   Amos A. Hari, et al.

Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a finite-element formulation. This approach is far more robust, versatile, and powerful than existing methods, thus allowing for more sophisticated computations and the study of problems that could not previously be tackled. Importantly, existing procedures, element libraries and shape functions, which have been developed throughout the years in the context of engineering analysis and partial differential equations, may be directly employed for this purpose.


page 1

page 2

page 3

page 4


Symmetrized two-scale finite element discretizations for partial differential equations with symmetric solutions

In this paper, a symmetrized two-scale finite element method is proposed...

Fireshape: a shape optimization toolbox for Firedrake

We introduce Fireshape, an open-source and automated shape optimization ...

Extended framework of Hamilton's principle applied to Duffing oscillation

The paper begins with a novel variational formulation of Duffing equatio...

Efficient simulation of DC-DC switch-mode power converters by multirate partial differential equations

In this paper, Multirate Partial Differential Equations (MPDEs) are used...

Parameter robust preconditioning by congruence for multiple-network poroelasticity

The mechanical behaviour of a poroelastic medium permeated by multiple i...

Towards Automated Design of Riboswitches

Experimental screening and selection pipelines for the discovery of nove...

Please sign up or login with your details

Forgot password? Click here to reset