| 1. |
- Akrivis, Georgios, et al.
(författare)
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Linearly implicit finite element methods for the time-dependent Joule heating problem
- 2005
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 45:3, s. 429-442
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Tidskriftsartikel (refereegranskat)abstract
- Completely discrete numerical methods for a nonlinear elliptic-parabolic system, the time-dependent Joule heating problem, are introduced and analyzed. The equations are discretized in space by a standard finite element method, and in time by combinations of rational implicit and explicit multistep schemes. The schemes are linearly implicit in the sense that they require, at each time level, the solution of linear systems of equations. Optimal order error estimates are proved under the assumption of sufficiently regular solutions.
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| 2. |
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| 3. |
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| 4. |
- Carleson, Lennart
(författare)
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Computations in pure mathematics
- 2006
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 46:SUPPL. 5, s. S19-S20
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Tidskriftsartikel (refereegranskat)
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| 5. |
- Cohen, David, et al.
(författare)
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Numerical energy conservation for multi-frequency oscillatory differential equations
- 2005
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 45:2, s. 287-305
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Tidskriftsartikel (refereegranskat)abstract
- The long-time near-conservation of the total and oscillatory energies of numerical integrators for Hamiltonian systems with highly oscillatory solutions is studied in this paper. The numerical methods considered are symmetric trigonometric integrators and the Stormer-Verlet method. Previously obtained results for systems with a single high frequency are extended to the multi-frequency case, and new insight into the long-time behaviour of numerical solutions is gained for resonant frequencies. The results are obtained using modulated multi-frequency Fourier expansions and the Hamiltonian-like structure of the modulation system. A brief discussion of conservation properties in the continuous problem is also included.
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| 6. |
- Elden, Lars, 1944-, et al.
(författare)
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Minimization of linear functionals defined on solutions of large-scale discrete Ill-posed problems
- 2005
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 45:2, s. 329-340
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Tidskriftsartikel (refereegranskat)abstract
- The minimization of linear functionals defined on the solutions of discrete ill-posed problems arises, e.g., in the computation of confidence intervals for these solutions. In 1990, Eldén proposed an algorithm for this minimization problem based on a parametric programming reformulation involving the solution of a sequence of trust-region problems, and using matrix factorizations. In this paper, we describe MLFIP, a large-scale version of this algorithm where a limited-memory trust-region solver is used on the subproblems. We illustrate the use of our algorithm in connection with an inverse heat conduction problem.
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| 7. |
- Elden, Lars
(författare)
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Solving quadratically constrained least squares problems using a differential-geometric approach
- 2002
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Ingår i: BIT Numerical Mathematics. - 0006-3835 .- 1572-9125. ; 42:2, s. 323-335
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Tidskriftsartikel (refereegranskat)abstract
- A quadratically constrained linea least squares problem is usually solved using a Lagrange multiplier for the constraint and then solving iteratively a nonlinear secular equation for the optimal Lagrange multiplier. It is well-known that, due to the closeness to a pole for the secular equation, standard methods for solving the secular equation can be slow, and sometimes it is not easy to select a good starting value for the iteration. The problem can be reformulated as that of minimizing the residual of the least squares problem on the unit sphere. Using a differential-geometric approach we formulate Newton's method on the sphere, and thereby avoid the difficulties associated with the Lagrange multiplier formulation. This Newton method on the sphere can be implemented efficiently, and since it is easy to find a good starting value for the iteration, and the convergence is often quite fast, it has a clear advantage over the Lagrange multiplier method. A numerical example is given.
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| 8. |
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| 9. |
- Englund, Jonas, et al.
(författare)
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A comparison of splittings and integral equation solvers for a nonseparable elliptic equation
- 2004
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 44:4, s. 675-697
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Tidskriftsartikel (refereegranskat)abstract
- Iterative numerical schemes for solving the electrostatic partial differential equation with variable conductivity, using fast and high-order accurate direct methods for preconditioning, are compared. Two integral method schemes of this type, based on previously suggested splittings of the equation, are proposed, analyzed, and implemented. The schemes are tested for large problems on a square. Particular emphasis is paid to convergence as a function of geometric complexity in the conductivity. Differences in performance of the schemes are predicted and observed in a striking manner.
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| 10. |
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