1 Introduction
1.1 Motivation  source of the boundary error
1.2 Existing approaches to reduce the resonance error
1.3 Notations and definitions
2 A modified elliptic approach
2.1 Relation with parabolic cell problems
3 Exponential decay of the resonance error for the modified elliptic approach
4 Approximation of the exponential operator
4.1 Spectral truncation
4.2 Approximation by the Arnoldi method
4.3 Approximation of the cell problem and computational cost
5 Numerical tests
Acknowledgments
The authors are grateful to Stefano Massei and Kathryn Lund for helpful discussion. This research is partially supported by Swiss National Science Foundation, grant no. .
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