An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications
Abstract Partial Differential Equations (PDEs) are fundamental to model different
phenomena in science and engineering mathematically. Solving them is a crucial step …
phenomena in science and engineering mathematically. Solving them is a crucial step …
Towards higher-order accurate mass lumping in explicit isogeometric analysis for structural dynamics
We present a mass lumping approach based on an isogeometric Petrov–Galerkin method
that preserves higher-order spatial accuracy in explicit dynamics calculations irrespective of …
that preserves higher-order spatial accuracy in explicit dynamics calculations irrespective of …
The variational collocation method
H Gomez, L De Lorenzis - Computer Methods in Applied Mechanics and …, 2016 - Elsevier
We propose the variational collocation method for the numerical solution of partial
differential equations. The conceptual basis is the establishment of a direct connection …
differential equations. The conceptual basis is the establishment of a direct connection …
The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements
We explore the use of the non-symmetric Nitsche method for the weak imposition of
boundary and coupling conditions along interfaces that intersect through a finite element …
boundary and coupling conditions along interfaces that intersect through a finite element …
Isogeometric collocation for phase-field fracture models
Phase-field models based on the variational formulation for brittle fracture have recently
been shown capable of accurately and robustly predicting complex crack behavior. Their …
been shown capable of accurately and robustly predicting complex crack behavior. Their …
Automatically imposing boundary conditions for boundary value problems by unified physics-informed neural network
Exact boundary conditions (BCs) imposition technique is widely used in physics-informed
neural networks (PINNs) for solving boundary value problems (BVPs). In this regard, the …
neural networks (PINNs) for solving boundary value problems (BVPs). In this regard, the …
Lagrange extraction and projection for NURBS basis functions: A direct link between isogeometric and standard nodal finite element formulations
D Schillinger, PK Ruthala… - International Journal for …, 2016 - Wiley Online Library
We introduce Lagrange extraction and projection that link a C0 nodal basis with a smooth B‐
spline basis. Our technology is equivalent to Bézier extraction and projection but offers an …
spline basis. Our technology is equivalent to Bézier extraction and projection but offers an …
Critical assessment of different mass lumping schemes for higher order serendipity finite elements
S Duczek, H Gravenkamp - Computer Methods in Applied Mechanics and …, 2019 - Elsevier
An efficient and robust finite element-based transient analysis of structures is important in
many engineering applications. In this context, a diagonal or lumped mass matrix is an …
many engineering applications. In this context, a diagonal or lumped mass matrix is an …
Orthogonal collocation revisited
LC Young - Computer Methods in Applied Mechanics and …, 2019 - Elsevier
Abstract 2018 marked the 80th anniversary of Lanczos (1938) and 2017 was the 50th
anniversary of Villadsen and Stewart (1967), both seminal works in development of the …
anniversary of Villadsen and Stewart (1967), both seminal works in development of the …
A new family of higher-order time integration algorithms for the analysis of structural dynamics
For the development of a new family of implicit higher-order time integration algorithms,
mixed formulations that include three time-dependent variables (ie, the displacement …
mixed formulations that include three time-dependent variables (ie, the displacement …