| 1. |
- Almquist, Martin, et al.
(författare)
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Order-preserving interpolation for summation-by-parts operators at nonconforming grid interfaces
- 2019
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Ingår i: SIAM Journal of Scientific Computing. - : Society for Industrial and Applied Mathematics Publications. - 1064-8275 .- 1095-7197. ; 41:2, s. A1201-A1227
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Tidskriftsartikel (refereegranskat)abstract
- We study nonconforming grid interfaces for summation-by-parts finite difference methods applied to partial differential equations with second derivatives in space. To maintain energy stability, previous efforts have been forced to accept a reduction of the global convergence rate by one order, due to large truncation errors at the nonconforming interface. We avoid the order reduction by generalizing the interface treatment and introducing order-preserving interpolation operators. We prove that, given two diagonal-norm summation-by-parts schemes, order-preserving interpolation operators with the necessary properties are guaranteed to exist, regardless of the grid-point distributions along the interface. The new methods retain the stability and global accuracy properties of the underlying schemes for conforming interfaces.
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| 2. |
- Eriksson, Gustav, et al.
(författare)
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Boundary and interface methods for energy stable finite difference discretizations of the dynamic beam equation
- 2023
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Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 476
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Tidskriftsartikel (refereegranskat)abstract
- We consider energy stable summation by parts finite difference methods (SBP-FD) for the homogeneous and piecewise homogeneous dynamic beam equation (DBE). Previously the constant coefficient problem has been solved with SBP-FD together with penalty terms (SBP-SAT) to impose boundary conditions. In this work, we revisit this problem and compare SBP-SAT to the projection method (SBP-P). We also consider the DBE with discontinuous coefficients and present novel SBP-SAT, SBP-P, and hybrid SBP-SAT-P discretizations for imposing interface conditions. To demonstrate the methodology for two-dimensional problems, we also present a discretization of the piecewise homogeneous dynamic Kirchoff-Love plate equation based on the hybrid SBP-SAT-P method. Numerical experiments show that all methods considered are similar in terms of accuracy, but that SBP-P can be more computationally efficient (less restrictive time step requirement for explicit time integration methods) for both the constant and piecewise constant coefficient problems.
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| 3. |
- Ljungberg Rydin, Ylva, 1992-, et al.
(författare)
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High-order finite difference method for the Schrödinger equation on deforming domains
- 2021
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Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 443
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Tidskriftsartikel (refereegranskat)abstract
- A high-order finite difference discretisation of the Schrödinger equation on do- mains that deform in time is presented. For the domain deformation, a time- dependent coordinate transformation is used. The utilisation of summation- by-parts finite difference operators, combined with boundary conditions im- posed weakly by a penalty technique, leads to a provably stable scheme. The convergence properties of the scheme are verified by numerical computations. The capabilities of the numerical scheme is demonstrated by simulations of Berry phases in deforming quantum billiards.
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| 4. |
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| 5. |
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| 6. |
- Nystrand, Thomas, et al.
(författare)
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Coarse-Graining Approach to Atomistic SpinDynamics
- 2015
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Ingår i: ULTRAFAST MAGNETISM I. - Cham : Springer International Publishing. - 9783319077437 - 9783319077420 ; , s. 162-165
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Konferensbidrag (refereegranskat)abstract
- We introduce a coarse-graining approach to study the movement of a Domain Wall (DW) under the influence of a spin polarized current, in the framework of atomistic spin dynamics. An increase in performance of up to 35% is obtained. We show the dependence of the method on both exchange range and temperature effects.
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| 7. |
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| 8. |
- Tazhimbetov, Nurbek, et al.
(författare)
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Simulation of flexural-gravity wave propagation for elastic plates in shallow water using an energy-stable finite difference method with weakly enforced boundary and interface conditions
- 2023
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 493
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Tidskriftsartikel (refereegranskat)abstract
- We introduce an energy stable, high-order-accurate finite difference approximation of the dynamic, pure bending Kirchhoff plate equations for complex geometries and spatially variable properties. We utilize the summation-by-parts (SBP) framework to discretize the biharmonic operator with variable coefficients, with attention given to free and clamped boundary conditions and corner conditions. Energy conservation is established by combining SBP boundary closures with weak enforcement of the boundary and interface conditions using a penalty (simultaneous approximation term, SAT) technique. Then we couple the plate equations to the shallow water equations to study flexural-gravity wave propagation, and prove that the semi-discrete system of equations is self-adjoint. We demonstrate the stability and accuracy properties of the method on curvilinear multiblock grids using the method of manufactured solutions. The method, which we provide in an open-source code, is then used to model ocean wave interactions with the Thwaites Glacier and Pine Island Ice Shelf in the Amundsen Sea off the coast of West Antarctica.
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| 9. |
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| 10. |
- Werpers, Jonatan
(författare)
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Finite Difference Methods for Wave Dominated Problems
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Wave models are an important class of models that describe many diverse phenomena such as sound waves, fluid flow, and quantum mechanics. These models are often described mathematically as partial differential equations (PDE). Often these equations do not admit solutions on closed-form and then the only option to study them is numerical methods. These numerical methods must be robust, accurate, and efficient. For spatial discretizations, it is known that higher-order finite-difference methods are efficient, but they often complicate achieving robustness.In this thesis, we focus on high-order finite-difference methods for solving these wave-dominated PDEs. We use the summation-by-parts (SBP) framework together with simultaneous approximation terms (SAT) for the boundary conditions to prove stability and robustness. This results in efficient numerical methods that are known to converge to the correct solution.The work in this thesis aims to broaden the scope of these finite-difference methods in different ways. In Paper I and III the framework is extended to two dispersive wave equations, solving challenges arising in both the spatial discretization as well as the time integration. The geometric flexibility of the methods is enhanced for the linear Euler equation and the Schrödinger equation in Paper II and VI by studying both stationary and time-dependent curvilinear grids. Paper IV shows how to use the framework to combine two models to describe and simulate a coupled physical system. In paper V we address a deficiency in the methodology around non-matching grids, showing a way to improve the accuracy and get faster convergence.
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