Solving high-wavenumber and heterogeneous Helmholtz equations presents a longstanding challenge in scientific computing. In this paper, we introduce a deep learning-enhanced multigrid solver to address this issue. By ...
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In this paper, we apply the practical GADI-HS iteration as a smoother in algebraic multigrid (AMG) method for solving second-order non-selfadjoint elliptic problem. Additionally, we prove the convergence of the derive...
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Recently, designing neural solvers for large-scale linear systems of equations has emerged as a promising approach in scientific and engineering computing. This paper first introduce the Richardson(m) neural solver by...
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In this work, we propose an efficient nullspace-preserving saddle search (NPSS) method for a class of phase transitions involving translational invariance, where the critical states are often degenerate. The NPSS meth...
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In this work, we propose an efficient nullspace-preserving saddle search (NPSS) method for a class of phase transitions involving translational invariance, where the critical states are often degenerate. The NPSS meth...
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In this paper, we propose a conservative nonconforming virtual element method for the full stationary incompressible magnetohydrodynamics model. We leverage the virtual element satisfactory divergence-free property to...
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This paper proposes an efficient general alternating-direction implicit (GADI) framework for solving large sparse linear systems. The convergence property of the GADI framework is discussed. Most of existing ADI metho...
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Matrix splitting iteration methods play a vital role in solving large sparse linear systems. Their performance heavily depends on the splitting parameters, however, the approach of selecting optimal splitting paramete...
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Finding index-1 saddle points is crucial for understanding phase transitions. In this work, we propose a simple yet efficient approach, the spring pair method (SPM), to accurately locate saddle points. Without requiri...
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The elliptic problem with nonlocal boundary condition is widely applied in the field of science and engineering. Firstly, we construct a linear finite element scheme for the nonlocal boundary problem, and derive the o...
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The elliptic problem with nonlocal boundary condition is widely applied in the field of science and engineering. Firstly, we construct a linear finite element scheme for the nonlocal boundary problem, and derive the optimal L 2 error estimate. Then, based on the quadratic finite element and the extrapolation linear finite element methods, we present a composite scheme, and prove that it is convergent order three. Furthermore, we design an upper triangular preconditioning algorithm for the linear finite element discrete system. Finally, numerical results not only validate that the new algorithm is efficient, but also show that the new scheme is convergent order three, furthermore order four on uniform grids.
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