linear parabolic equations
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Linear Convergence of Parareal Algorithm for Semilinear Parabolic Equations
arXiv:2606.03516v1 Announce Type: new Abstract: Long-time simulations of evolution equations present substantial computational challenges due to the inherently sequential nature of conventional time-stepping schemes. The parareal method, a leading parallel-in-time (PinT) algorithm, offers a promising approach to overcome the challenge by introducing concurrency in the time domain. While its convergence theory is well-established for linear problems, extending the theory to nonlinear...
A fast reduced order method for linear parabolic inverse source problems
arXiv:2306.05677v2 Announce Type: replace Abstract: In this paper, we propose a novel, computationally efficient reduced order method to solve linear parabolic inverse source problems. Our approach provides accurate numerical solutions without relying on specific training data. The forward solution is constructed using a Krylov sequence, while the source term is recovered via the conjugate gradient (CG) method.
Structure-Preserving Quantum Method of Lines for Evolutionary PDEs with Mixed Boundary Conditions
arXiv:2606.03407v1 Announce Type: cross Abstract: We give detailed analysis and circuit design of structure-preserving quantum algorithms for second-order linear evolutionary PDEs, including parabolic equations and hyperbolic equations with mixed Dirichlet, Neumann, and periodic boundary conditions and source terms. While prior quantum algorithms usually neglect the stability problem from the PDE-to-ODE reduction, our method-of-lines approach investigates the boundary lifting via Coons...
A-priori error estimation for space-time Galerkin POD for linear evolution problems
arXiv:2604.22057v2 Announce Type: replace Abstract: In this paper, we propose an a-priori error estimate for the model order reduction (MOR) method of space-time proper orthogonal decomposition (space-time POD). The original space-time POD approach extends standard POD by reducing not only the space dimension but simultaneously the time dimension as well. The proposed a-priori error estimate is developed for a linear parabolic partial differential equation and estimates the error between the...