So, I found that in the original Bitcoin client there was a member variable vSpent in the class CWalletTX, however it appears that this is no longer the case in the new version. I know that the new Bitcoin client uses UTXO DB to store the unspent transactions. My question is that since LevelDB is a key-value database, and the UTXO key is derived from transaction outpoint, how does the client find the Txs that belongs to the wallet owner? Does it iterate over all unspent transactions and find those containing the public key of the receiver?
The wallet is to a large extent separate from the rest of the node software. One of the reasons for this is because of the (slow) progress towards a working SPV mode. This means the wallet cannot depend on access to the UTXO set, as it won't be available in non-validating nodes.
However, it isn't needed. The wallet maintains an index of all input prevouts inside the wallet. Every output that is seen in a block, is to a wallet address, and which is not in this index as the input for another wallet transaction, is spendable.