Related papers: A simple Python code for computing effective prope…
The Hodge decomposition provides a very powerful mathematical method for the analysis of 2D and 3D vector fields. It states roughly that any vector field can be $L^2$-orthogonally decomposed into a curl-free, divergence-free, and a harmonic…
A primitive problem of predicting the effective properties of composites is open boundary conditions. In this paper, Eshelby's transformation field method is developed to solve the open boundary problem of two-phase composites having…
We develop an accurate, highly efficient and scalable random batch Ewald (RBE) method to conduct simulations in the isothermal-isobaric ensemble (the NPT ensemble) for charged particles in a periodic box. After discretizing the Langevin…
A Waveguide Port Boundary Condition (WPBC) based on the restriction of the approximation space is presented in the context of Finite Element Analysis. As well as reducing the computational domain in the same manner as the traditional WPBC,…
This paper presents a 55-line code written in python for 2D and 3D topology optimization (TO) based on the open-source finite element computing software (FEniCS), equipped with various finite element tools and solvers. PETSc is used as the…
Partial Differential Equations (PDEs) are fundamental for modeling physical systems, yet solving them in a generic and efficient manner using machine learning-based approaches remains challenging due to limited multi-input and multi-scale…
The estimation of patient-specific tissue properties in the form of model parameters is important for personalized physiological models. However, these tissue properties are spatially varying across the underlying anatomical model,…
Given that the physical properties of polymeric liquids extend on a wide range of lengthscales, it is computationally convenient to represent them by coarse-grained (CG) descriptions at various granularities to investigate local and global…
When designing correct-by-construction controllers for autonomous collectives, three key challenges are the task specification, the modelling, and its use at practical scale. In this paper, we focus on a simple yet useful abstraction for…
We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson…
Point containment queries on trimmed surfaces are fundamental to CAD modeling, solid geometry processing, and surface tessellation. Existing approaches such as ray casting and generalized winding numbers often face limitations in robustness…
While the recursive property of entropy is well known in information theory, it is rarely utilized in thermodynamics, despite entropy originating in this field. Moreover, computational tools to implement this concept within first-principles…
We introduce and analyze a virtual element method (VEM) for the Helmholtz problem with approximating spaces made of products of low order VEM functions and plane waves. We restrict ourselves to the 2D Helmholtz equation with impedance…
Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate…
A property $\Pi$ on a finite set $U$ is \emph{monotone} if for every $X \subseteq U$ satisfying $\Pi$, every superset $Y \subseteq U$ of $X$ also satisfies $\Pi$. Many combinatorial properties can be seen as monotone properties. The problem…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet…
We optimize Hockney and Eastwood's Particle-Particle Particle-Mesh (P3M) algorithm to achieve maximal accuracy in the electrostatic energies (instead of forces) in 3D periodic charged systems. To this end we construct an optimal influence…
A fundamental characteristic common to both human vision and natural language is their compositional nature. Yet, despite the performance gains contributed by large vision and language pretraining, we find that: across 7 architectures…
Flexible piezoelectric devices made of polymeric materials are widely used for micro- and nano-electro-mechanical systems. In particular, numerous recent applications concern energy harvesting. Due to the importance of computational…