| 1. |
- Engström, Christian, et al.
(författare)
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A spectral projection based method for the numerical solution of wave equations with memory
- 2022
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Ingår i: Applied Mathematics Letters. - : Elsevier. - 0893-9659 .- 1873-5452. ; 127
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we compare two approaches to numerically approximate the solution of second-order Gurtin-Pipkin type of integro-differential equations. Both methods are based on a high-order Discontinous Galerkin approximation in space and the numerical inverse Laplace transform. In the first approach, we use functional calculus and the inverse Laplace transform to represent the solution. The spectral projections are then numerically computed and the approximation of the solution of the time-dependent problem is given by a summation of terms that are the product of projections of the data and the inverse Laplace transform of scalar functions. The second approach is the standard inverse Laplace transform technique. We show that the approach based on spectral projections can be very efficient when several time points are computed, and it is particularly interesting for parameter-dependent problems where the data or the kernel depends on a parameter.
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| 2. |
- Engström, Christian, et al.
(författare)
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Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications
- 2016
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Ingår i: Computers and Mathematics with Applications. - : Elsevier. - 0898-1221 .- 1873-7668. ; 72:4, s. 952-973
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Tidskriftsartikel (refereegranskat)abstract
- We present a-posteriori analysis of higher order finite element approximations (hp-FEM) for quadratic Fredholm-valued operator functions. Residual estimates for approximations of the algebraic eigenspaces are derived and we reduce the analysis of the estimator to the analysis of an associated boundary value problem. For the reasons of robustness we also consider approximations of the associated invariant pairs. We show that our estimator inherits the efficiency and reliability properties of the underlying boundary value estimator. As a model problem we consider spectral problems arising in analysis of photonic crystals. In particular, we present an example where a targeted family of eigenvalues cannot be guaranteed to be semisimple. Numerical experiments with hp-FEM show the predicted convergence rates. The measured effectivities of the estimator compare favorably with the performance of the same estimator on the associated boundary value problem. We also present a benchmark estimator, based on the dual weighted residual (DWR) approach, which is more expensive to compute but whose measured effectivities are close to one.
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| 3. |
- Engström, Christian, et al.
(författare)
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Higher Order Composite DG approximations of Gross–Pitaevskii ground state : benchmark results and experiments
- 2022
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 400
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Tidskriftsartikel (refereegranskat)abstract
- Discontinuous Galerkin composite finite element methods (DGCFEM) are designed totackle approximation problems on complicated domains. Partial differential equationsposed on complicated domain are common when there are mesoscopic or local phenomena which need to be modelled at the same time as macroscopic phenomena. In thispaper, an optical lattice will be used to illustrate the performance of the approximationalgorithm for the ground state computation of a Gross–Pitaevskii equation, which isan eigenvalue problem with eigenvector nonlinearity. We will adapt the convergenceresults of Marcati and Maday 2018 to this particular class of discontinuous approximation spaces and benchmark the performance of the classic symmetric interior penaltyhp-adaptive algorithm against the performance of the hp-DGCFEM.
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| 4. |
- Engström, Christian, et al.
(författare)
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Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms
- 2023
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 425
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider the numerical inverse Laplace transform for distributed order time-fractional equations, where a discontinuous Galerkin scheme is used to discretize the problem in space. The success of Talbot’s approach for the computation of the inverse Laplace transform depends critically on the problem’s spectral properties and we present a method to numerically enclose the spectrum and compute resolvent estimates independent of the problem size. The new results are applied to time-fractional wave and diffusion-wave equations of distributed order.
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| 5. |
- Giani, Stefano, et al.
(författare)
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khp-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory
- 2023
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 429
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we present an adaptive spectral projection based finite element method to numerically approximate the solution of the wave equation with memory. The adaptivity is not restricted to the mesh (-adaptivity), but it is also applied to the size of the computed spectrum (-adaptivity). The meshes are refined using a residual based error estimator, while the size of the computed spectrum is adapted using the norm of the error of the projected data. We show that the approach can be very efficient and accurate.
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| 6. |
- Maxwell, Tania L., et al.
(författare)
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Global dataset of soil organic carbon in tidal marshes
- 2023
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Ingår i: Scientific Data. - : Springer Nature. - 2052-4463. ; 10:1
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Tidskriftsartikel (refereegranskat)abstract
- Tidal marshes store large amounts of organic carbon in their soils. Field data quantifying soil organic carbon (SOC) stocks provide an important resource for researchers, natural resource managers, and policy-makers working towards the protection, restoration, and valuation of these ecosystems. We collated a global dataset of tidal marsh soil organic carbon (MarSOC) from 99 studies that includes location, soil depth, site name, dry bulk density, SOC, and/or soil organic matter (SOM). The MarSOC dataset includes 17,454 data points from 2,329 unique locations, and 29 countries. We generated a general transfer function for the conversion of SOM to SOC. Using this data we estimated a median (± median absolute deviation) value of 79.2 ± 38.1 Mg SOC ha−1 in the top 30 cm and 231 ± 134 Mg SOC ha−1 in the top 1 m of tidal marsh soils globally. This data can serve as a basis for future work, and may contribute to incorporation of tidal marsh ecosystems into climate change mitigation and adaptation strategies and policies.
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