Related papers: PyDEC: Software and Algorithms for Discretization …
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes…
SfePy (Simple finite elements in Python) is a software for solving various kinds of problems described by partial differential equations in one, two or three spatial dimensions by the finite element method. Its source code is mostly (85\%)…
The dynamic mode decomposition (DMD) is a simple and powerful data-driven modeling technique that is capable of revealing coherent spatiotemporal patterns from data. The method's linear algebra-based formulation additionally allows for a…
In recent years, edge computing (EC) has attracted great attention for its high-speed computing and low-latency characteristics. However, there are many challenges in the implementation of EC. Firstly, user's privacy has been raised as a…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer…
Computing intrinsic distances on discrete surfaces is at the heart of many minimization problems in geometry processing and beyond. Solving these problems is extremely challenging as it demands the computation of on-surface distances along…
The advancement of domain reduction techniques has significantly enhanced the performance of solvers in mathematical programming. This paper delves into the impact of integrating convexification and domain reduction techniques within the…
We present a discrete exterior calculus (DEC) based discretization scheme for incompressible two-phase flows. Our physically-compatible exterior calculus discretization of single phase flow is extended to simulate immiscible two-phase flows…
Outlier detection is an important task for various data mining applications. Current outlier detection techniques are often manually designed for specific domains, requiring large human efforts of database setup, algorithm selection, and…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
We describe the program pySecDec, which factorises endpoint singularities from multi-dimensional parameter integrals and can serve to calculate integrals occurring in higher order perturbative calculations numerically. We focus on the new…
We have developed PyTIE (Python Topological Indices Expressions) which is defined as the collections of Python packages such as PyTIE D, PyTIE DS, PyTIE SMS DE, and PyTIE SMS DSE, which are open-source software packages and cross-platform…
Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology,…
Python libraries often need to maintain a stable public API even as internal implementations evolve, gain new backends, or depend on heavy optional libraries. In Python, where internal objects are easy to inspect and import, users can come…
A mathematical programming problem with affine equilibrium constraints (AMPEC) is a bilevel programming problem where the lower one is a parametric affine variational inequality. We formulate some classes of bilevel programming in forms of…
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large size. Based on a common graph-based formalism, we analyze existing data structures for simplicial…
This paper introduces open-source contributions designed to accelerate research in volumetric multi-material additive manufacturing and metamaterial design. We present a flexible Python-based API facilitating parametric expression of…
In this work we propose a high-order structure-preserving discretization of the cold plasma model which describes the propagation of electromagnetic waves in magnetized plasmas. By utilizing B-Splines Finite Elements Exterior Calculus, we…