Efficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:msub><mml:mi>W</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math> and Bethe-Salpeter equation calculat

The combination of two-dimensional materials into heterostructures offers new opportunities for the design of optoelectronic devices with tunable properties. However, computing electronic and optical properties of such systems using state-of-the-art methodology is challenging due to their large unit cells. This is particularly so for highly precise all-electron calculations within the framework of many-body perturbation theory, which come with high computational costs. Here, we extend an approach that allows for the efficient calculation of the noninteracting polarizability, previously developed for plane wave basis sets, to the (linearized) augmented plane wave method. This approach is based on an additive ansatz, which computes and superposes the polarizabilities of the individual components in their respective unit cells. We implement this formalism in the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>G</a:mi><a:mn>0</a:mn></a:msub><a:msub><a:mi>W</a:mi><a:mn>0</a:mn></a:msub></a:mrow></a:math> module of the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi mathvariant="monospace">exciting</b:mi></b:math> code and implement an analogous approach for BSE calculations. This allows the calculation of highly precise optical spectra at low cost. So-obtained results of the quasiparticle band structure and optical spectra are demonstrated for bilayer <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>WSe</d:mi><d:mn>2</d:mn></d:msub></d:math> and pyridine@<e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>MoS</e:mi><e:mn>2</e:mn></e:msub></e:math> in comparison with exact reference calculations.