Related papers: Higher-order multi-scale method for high-accuracy …
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
The aim of this work is the numerical homogenization of a parabolic problem with several time and spatial scales using the heterogeneous multiscale method. We replace the actual cell problem with an alternate one, using Dirichlet boundary…
The emergence of second-generation high temperature superconducting tapes has favored the development of large-scale superconductor systems. The mathematical models for superconductors have evolved from simple analytical models to complex…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
Accurate analytical and numerical modeling of multiscale systems is a daunting task. The need to properly resolve spatial and temporal scales spanning multiple orders of magnitude pushes the limits of both our theoretical models as well as…
A straightforward algorithm for the symbolic computation of higher-order symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the…
A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequencies is presented for the transient analysis of structural dynamic problems. The amount of numerical dissipation is controlled…
Accurate predictions of thermo-mechanically coupled process in metals can lead to a reduction of cost and an increase of productivity in manufacturing processes such as forming. For modeling these coupled processes with the finite element…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
A multiscale asymptotic homogenization method for periodic microstructured materials in presence of thermoelasticity with periodic spatially dependent one relaxation time is introduced. The asymptotic expansions of the micro-displacement…
An extension of the multi-level hp Finite Cell Method is proposed for the simulation of thermoviscoplastic problems with temperature-dependent material behavior. The approach combines hierarchical adaptive refinement with a non-negative…
In this paper we present a novel framework for obtaining high-order numerical methods for scalar conservation laws in one-space dimension for both the homogeneous and non-homogeneous case. The numerical schemes for these two settings are…
In this work, we introduce a new Hybrid High-Order method for the numerical simulation of fracture propagation based on phase-field models. The proposed method supports general meshes made of polygonal/polyhedral elements, which provides…
In this paper, we introduce a fourth-order accurate finite element method for incompressible variable density flow. The method is implicit in time and constructed with the Taylor series technique, and uses standard high-order Lagrange basis…
Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…
Nonlinear time-history evolution problems employing high-fidelity physical models are essential in numerous scientific domains. However, these problems face a critical dual bottleneck: the immense computational cost of time-stepping and the…
This paper presents a computationally efficient method for the optimal design of silica aerogel porous material systems, balancing thermal insulation performance with mechanical stability under stress concentrations. The proposed approach…
We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dynamics. We show that the proposed HDG method is well-posed…
A novel mixed-hybrid method for Kirchhoff-Love shells is proposed that enables the use of classical, possibly higher-order Lagrange elements in numerical analyses. In contrast to purely displacement-based formulations that require higher…